# Die Beschriinkung auf "nichtlineare" Programmierung ist so zu verstehen.

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1 BIBLIOGRAPHIE Die ~m folgenden aufgefiihrten Publikationen sind gedacht als Materialsammlung zu einer umfassenden Bestandesaufnahme der nichtlinearen Programmierung nebst ihren Grundlagen und Anwendungen. Die Ausarbeitung wird an anderer Stelle erfolgen. Einstweilen soli diese Sammlung als Arbeitsinstrument einem grosseren Kreis zur Verfiigung gestellt werden. Dies geschieht in der Hoffnung. dass sie dem Beniitzer ein einigermassen zuverhissiges Bild von der Aktivitiit auf diesem Gebiet vermittle. und dass sie dem selbst in der Forschung Tiitigen helfe. unnotige Duplikationen zu vermeiden. Bei den Arbeiten zur Theorie der nichtlinearen Programmierung wurde Vollstiindigkeit angestrebt; dagegen mag eine gewisse Unausgeglichenheit bei der Beriicksichtigung der verschiedenen Anwendungsgebiete daraus resultieren. dass die Sammlung anfiinglich nur zum privaten Gebrauch angelegt wurde. Die Beschriinkung auf "nichtlineare" Programmierung ist so zu verstehen. dass keine Arbeiten aufgenommen wurden. die lineare Programmierungsprobleme vorwiegend im Rahmen der linear en Algebra (Gauss-Jordan Elimination) abhandeln. Wohl aber wurden lineare Programme in abstrakten Riiumen beriicksichtigt. ebenso iterative Verfahren zur Losung linearer Programme (diese Verfahren lassen sich meist unschwer auf den konvexen Fall iibertragen). Auch bestimmte Anwendungen der linearen Programmierung. die in den auf die Bediirfnisse des Operations Research zugeschnittenen Darstellungen meist zu kurz kommen. wurden aufgenommen. Quadratische und gebrochen-lineare Programme wurden. allgemeinem Sprachgebrauch folgend. zur nichtlinear en Programmierung gerechnet und entsprechend beriicksichtigt. Nicht einbezogen wurden Arbeiten zur dynamischen. stochastiscl1en und ganzzahligen Programmierung. eben so blosse Rechenbeispiele.

2 Unter den theoretischen Anwendungen nehmen die numerische Analysis (insbesondere Approximationstheorie), Kontrolltheorie. Wirtschaftswissenschaften und Unternehmungsforschung den grossten Raum ein. (Hierbei ist darauf hinzuweisen. dass nicht alle zitierten Arbeiten die Beziehung zur mathematischen Programmierung explizite herstellen). Bei den Grundlagen schienen besonders wichtig: die Theorie konvexer Mengen und Funktionen, sowie Verfahren zur Optimierung einer Funktion ohne Nebenbedingungen. Die Titel der Arbeiten sind entweder im Original oder in englischer Uebersetzung wiedergegeben. Die Quellenangaben folgen dem Muster der "Mathematical Reviews". Insbesondere sind die verwendeten AbkUrzungen der Zeitschriften bis auf geringfugige Aenderungen den "Abbreviations of Names of Journals" am Schluss der Bande 34 (1967) bis ~ (1969) von "Mathematical Reviews" entnommen oder dem dort benutzten System nachgebildet. FUr die Transkription kyrillischer Eigennamen wurde gegenuber "Mathematical Reviews" eine mehr phonetische Schreibweise gewahlt, die Akzente UberflUssig macht. Die in Abschnitt B aufgefuhrten Sammelwerke werden in Abschnitt C nur durch Herausgabe und Erscheinungsjahr gekennzeichnet. z. B. [Abadie, 1967J Publikationen in Manuskriptform (sogenannte Reports) wurden nur vereinzelt aufgenommen, und nur in solchen Fallen, wo eine Veroffentlichung in anderer Form nicht nachzuweisen war. Hinweise auf etwaige Fehler sowie Erganzungsvorschlage werden an die folgende Anschrift erbeten: W. Oettli, IBM Forschungslaboratorium ZUrich, 8803 RUschlikon, Schweiz.

3 BIBLIOGRAPHY The references collected hereafter are intended to contain the rawmaterial of a comprehensive inventory of non-linear programming, including its foundations and applications. The decision to publish them in the present (and preliminary) form was made in the hope, that this will help the interested in keeping up with the activity going on in this field. Whereas the list of papers concerned with the very theory of non-linear programming should be reasonable complete, a certain "bias" regarding the selected applications may eventually be due to the subjective motivation which stood at the origin of this collection. The restriction to "non-linear" programming essentially is to mean, that papers handling linear programming problems within the framework of linear programming problems in abstract spaces were included, as well as iterative procedures for solving linear programs. Also included were quadratic and fractionally -linear programming. Dynamic, stochastic and integer programming are missing. Among the theoretical applications numerical analysis (especially approximation theory), control theory, economics and operations research playa dominant role. (At this point the reader should be warned that in the case of many of the quoted references he has to establish himself the connections with mathematical programming. ) Among the foundations convex functions and methods for unconstrained optimization take the largest part. The quotations follow the style of "Mathematical Reviews". Abbreviations of names of journals are the same as those given at the end of volumes 34 (1967) through ~ (1969) of "Mathematical Reviews". The transliteration of cyrillic names however ist slightly different from the system adopted by "Mathematical Reviews".

4 The collective volumes listed in section B are identified in section C only by name of editor and year of publication. e. g. [Abadie. 1967J. Any critical comments concerning errors or omissions are welcomed at the following address: W. Oettli. IBM Zurich Research Laboratory Ruschlikon. Switzerland.

5 SCHRIFTTUM ZUR NICHTLINEAREN PROGRAMMIERUNG NEBST VERW ANDTEN GEBIETEN REFERENCES IN NON-LINEAR PROGRAMMING AND RELATED AREAS A. Lehrbiicher und Monographien I Textbooks and monographs E. M. L. BEALE R. BELLMAN R. BELLMAN, S. DREYFUS C. BERGE C. BERGE C. BERGE, A. GHOUILA-HOURI T. BONNE SEN, W. FENCHEL J. C. G. BOOT R. BOUDAREL, J. DELMAS, p.. GUICHET Mathematic'al Programming in Practice. Pitman, London, Dynamic Programming. Princeton University Press, Princeton, Applied Dynamic Programming. Princeton University Press, Princeton, Espaces topologiques, fonctions multivoques. Dunod. Paris, Topological Spaces (Translated from the French). Oliver and Boyd, Edinburgh, Programmes, jeux et reseaux de transport. Dunod, Paris, Theorie der konvexen Kerper. Springer, Berlin, Chelsea, New York, Quadratic Programming. North-Holland, Amsterdam, Commande optimale des processus. Tome 2: Programmation non lineaire et ses applications. Dunod, Paris, 1968.

6 M. J. BOX~ D. DAVIES~ W. H. SWANN J. BRACKEN~ G. P. McCORMICK E. BURGER M. CANON~ C. CULLUM~ E. POLAK A. CHARNES~ W.W. COOPER E. W. CHENEY L. COLLATZ~ W. WETTERLING J. M. DANSKIN G. B. DANTZIG J. B. DENNIS M. DRESHER R. J. DUFFIN~ E. L. PETERSON~ C. ZENER H. G. EGGLESTON Nonlinear Optimization Techniques. Oliver and Boyd. London. (to appear). Selected Applications of Nonlinear Programming. Wiley. New York~ Einftihrung in die Theorie der Spiele. Walter de Gruyter~ Berlin Discrete Optimal Control. McGraw-Hill~ New York (to appear). Management Models and Industrial Applications of Linear Programming; 2 Vols. Wiley~ New York~ Introduction to Approximation Theory. McGraw-Hill.. New York Optimierungsaufgaben. Springer.. Berlin The Theory of Max-Min. Spring er.. Berlin Linear Programming and Extensions. Princeton University Press. Princeton~ Mathematical Programming and Electrical Networks. Wiley. New York Games of Strategy: Theory and Applications. Prentice-Hall. Englewood Cliffs.. N. J Geometric Programming-Theory and Application. Wiley.. New York Convexity. Cambridge University Press. Cambridge

7 W. FENCHEL A. V. FIACCO~ G. P. McCORMICK L. R. FORD~ D. R. FULKERSON Convex Cones, Sets, and Functions (Lecture Notes). Department of Mathematics.. Princeton University~ Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley~ New York, Flows in Networks. Princeton University Press.. Princeton~ R. FRISCH Theorie et appli Maxima et minima - cations economiques. Dunod.. Paris D. GALE A. A. GOLDSTEIN G. HADLEY H. HANCOCK H. KAPPLER S. KARLIN S. KARLIN~ L. S. SHAPLEY M. A. KRASNOSELSKII~ Ya. B. RUTICKII The Theory of Linear Economic Models. McGraw-Hill, New York Constructive Real Analysis. Harper & Row.. New York, Nonlinear and Dynamic Programming. Addison-Wesley. Reading.. Mass Theory of Maxima and Minima. Dover, New York Gradientenverfahren der nichtlinearen Programmierung (G6ttinger Wirtschafts- und Sozialwissenschaftliche Studien.. Band 5). Verlag Otto Schwarz. G6ttingen Mathematical Methods and Theory in Games.. Programming.. and Economics; 2 Vols. Addison- Wesley. Cambridge~ Mass. ~ Geometry of Moment Spaces. Memoirs Amer. Math. Soc... no. 12; American Mathematical Society.. Providence, R. I Convex Functions and Orlicz Spaces. Noordhoff.. Groningen~ 1961.

8 H. P. KONZI~ W. KRELLE H. P. KONZI~ H. G. TZSCHACH~ C. A. ZEHNDER O. L. MANGASARIAN J. C. C. M~KINSEY Nichtlineare Programmierung. Springer.. Berlin Numerische Methoden der mathematischen Optimierung. B. G. Teubner.. Stuttgart Nonlinear Programming. McGraw-Hill.. New York (to appear). Introduction to the Theory of. Games. McGraw-Hill.. New York.. i952. J.~. RICE The Approximation of Functions.. Vol. 1. Addison-Wesley. Reading. Mass V. RILEY.. S. I. GASS R. T. ROCKAFELLAR R. T. ROCKAFELLAR T. L. SAATY.. J. BRAM S. VAJDA F. A. VALENTINE D.J. WILDE D.J. WILDE.. C. S. BEIGHTLER G. ZOUTENDIJK Linear Programming and Associated Technique s. The John Hopkins Press.. Baltimore Monotone Processes of Convex and Concave Type. Memoirs Amer. Math. Soc no. 77; American Mathematical Society~ Providence. R.I Convex Analysis. Princeton University Press.. Princeton (to appear). Nonlinear Mathematics. McGraw-Hill.. New York Mathematical Programming. Addison-Wesley.. Reading. Mass Convex Sets. McGraw-Hill.. New York Optimum Seeking Methods. Prentice-Hall.. Englewood Cliffs.. N. J Foundations of Optimization. Prentice-Hall.. Englewood Cliffs.. N. J., Methods of Feasible Directions. Elsevier. Amsterdam

9 S. I. ZUKHOVITSK1J~ L. I. A VDEEV A S. I. ZUKHOVITSKIY. L. L AVDEYEVA Lineinoe i vypukloe programmirovanie. Izdatelstvo Nauka.. Moskva Linear and Convex Programming (translated from the Russian). Saunders.. Philadelphia B. Sammelbande I Collective Volumes J. ABADIE (ed.) K.J. ARROW. L. HURWICZ. H. UZAWA (eds.) A. V. BALAKRISHNAN. L. W. NEUSTADT (eds.) R. BELLMAN (ed.) P. BROISE. P. HUARD. J. SENTENAC G. B, DANTZIG. A. F. VEINOTT (eds.) R. FORTET. J. ABADIE.. J. BERNADAT.. M. COUR TILLOT.. J. -M. GAUTHIER.. F. GENUYS.. P. HUARD.. G. MATTHYS R. L. GRAVES.. Ph. WOLFE (eds.) Nonlinear Programming. North-Holland.. Amsterdam Studies in Linear and Non-linear Programming. Stanford University Press.. Stanford Mathematical Theory of Control. Academic Press. New York Mathematical Optimization T,=chniques. UniVersity of California Press" Berkeley" Decomposition des programmes mathematiques (Monographies de recherche operationnelle.. 6). Dunod. Paris Mathematics of the Decision Sciences. Part Lectures in Applied Mathematics.. Vol American Mathematical Society.. Providence.. R Mathematique des programmes economiques (Monographies de recherche operationnelle.. 1). Dunod. Paris, Recent Advances in Mathematical Programming. McGraw-Hill.. New York

10 D. C. HANDSCOMB (ed.) L. V. KANTOROVICH (ed.) T. C. KOOPMANS (ed.) H. W. KUHN (ed.) H. W. KUHN~ A. W. TUCKER (eds.) A. LAVI~ T. P. VOGL (eds.) A. PREKQPA (ed.) Ph. WOLFE (ed.) Methods of Numerical Approximation. Pergamon Press. Oxford Matematicheskoe programmirovanie. Izdatelstvo Nauka~ Moskva~ Activity Analysis of Production and Allocation. Wiley~ New York Proceedings of the Sixth International Symposium on Mathematical Programming. Princeton~ (to appear). Linear Inequalities and Related Systems. Annals of Mathematics Studies.. no. 38; Princeton University Press~ Princeton~ Recent Advances in Optimization Techniques. Wiley. New York~ Colloquium on Applications of Mathematics to Economics.. Budapest Akademiai Kiad6. Budapest The RAND Symposium on Mathematical Programming (Abstracts). RAND-Report R-351. The RAND Corporation. Santa Monica. Calif

11 C. Aufsatze / Articles ABADIE (J.): Elements de programmation mathematique. Note HR Electricite de France~ Direction des Etudes et Recherches~ : Probl~mes d'optimisation~ I. II. Laboratoire de Calcul numerique.. Institut Blaise Pascal~ Paris~ --- : Programmation mathematique. Actes du 5~me Congr~s AFIRO (Lille 1966)~ pp Association Fran<;<aise d'informatique et de Recherche Operationelle~ Paris : On the Kuhn-Tucker theorem. [l\.badie~ 1967J, pp ~ CARPENTIER (J.): Generalisation de la methode du gradient reduit de Wolfe au cas de contraintes non line aires. Note HR 7.262/0. Electricite de France~ Direction des Etudes et Recherches~ ~ HENSGEN (C.): La methode du gradient reduit generalise. Rapport CAE/RT/2057. Compagnie Europeenne d'automatisme Electronique.. Paris~ ~ HUARD (P.) et al.: La programmation quadr ati que. Actes du 1er Congr~s AFCAL (Grenoble 1960).. pp Gauthier- Villars~ Paris~ ABLOW (C. M.).. BRIGHAM (G.): An analog solution of programming problems. Operations Res. l (1955) ABRHAM (J.): An approximate method for nonlinear programming (Czech). Casopis Pest. Mat. ~ (1958) : An approximate method for convex programming. Econometrica ~ (1961)~ : The multiplex method and its application to concave programming. Czechoslovak Math. J. 12 (1962)

12 : An approximate method for solving a continuous-time allocation problem. CORE Discussion Paper no Center for Operations Research and Econometrics, Universite Catholique de Louvain~ AGGARWAL (S. P.): A simplex technique for a particular convex programming problem. J. Canad. Operational Res. Soc. (CORS J.)! (1966)~ Stability of the solution to a linear fractional functional programming problem. Z. angew. Math. Mech. 46 (1966)~ : A note on quasiconvex programming. Metrika ~ (1968), : Standard error fractional functional programming. Istanbul Univ. Fen Fak. Mec. Sere A ~ (1965),45-51 (issued 1968). ---.; SW ARUP (K.): Fractional functionals programming with a quadratic constraint. Operations Res. 14 (1966), AGGERI (J. -C. l: Les fonctions convexes continues et Ie theor~me Krein-Milman. C. R. Acad. Sci. Paris sere A. 262 (1966), de --- ~ LESCARRET (C.): Fonctions convexes duales associees ~ un couple d' ensembles mutuellement polaires. C. R. Acad. Sci. Paris 260 (1965), AGMON (8): The relaxation method for linear inequalities. Canad. J. Math. ~ (1954), AKAIKE (ll): On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method. Ann. Inst. Statist. Math.!!. (1959)~ AKILOV (G. P.)~ KANTOROVICH (L. V.)~ RUBINSHTEIN (G. Sh.): Extremal states and extremal controls (Russian). Vestnik Leningrad. Univ. 22 (1967)~ no. 7, SIAM J. Control ~ (1967): (English transl.). -- ~ RUBINOV (A. M.): The method of successive approximations for determining the polynomial of best approximation (Russian). Dokl.Akad. Nauk SSSR 157 (1964), Soviet Math. Dokl. ~ (1964), (English transl.).

13 AKKEL (T.): A standard program for solution of a general nonlinear programming problem (Russian). Trudy VyCisl. Centra Tartu. Gos. Univ no. 2~ ALTMAN (M.): Stationary points in non-linear programming. Bull. Acad. Pol on. Sci. sere Sci. Math. Astronom. Phys. 12 (1964) : A feasible direction method for solving the nonlinear programming problem. Bull. Acad. Pol on. Sci. sere Sci. Math. Astronom. Phys. g (1964)~ : A generalized gradient method of minimizing a functional on a Banach space. Mathematica (Cluj) ~ (1966)~ : Generalized gradient methods of mlffimlzmg a functional. Bull. Acad. Polon. Sci. sere Sci. Math. Astronom. Phys. 14 (1966)~ : A generalized gradient method for the conditional minimum of a functional. Bull. Acad. Polon. Sci. sere Sci. Math. Astronom. Phys. 14 (1966)~ : A generalized gradient method with self-fixing step size for the conditional minimum of a functional. Bull. Acad. Polon. Sci. sere Sci. Math. Astronom. Phys. i5 (1967)~ : A generalized gradient method for the conditional extremum of a function. Bull. Acad. Polon. Sci. sere Sci. Math. Astronom. Phys. 15 (1967) : Bilinear Programming Bull. Acad. Polon. Sci. sere Sci. Math. Astronom. Phys. 16 (1968)~ ANDREEV (N. I.): A method of solution of certain problems in nonlinear programming (Russian). Izv. Akad. Nauk SSSR Tekhn. Kibernet no : Non-linear programming in the investigation of optimal automatic control systems. In: Proceedings of the International Federation of Automatic Control Congress (Basle 1963). Butterworth~ London~ 1964.

14 de ANGELIS (V.): Ricerca del mlffimo valoree di una funzione convessa separabile sottoposta a vincoli lineari. Giorn. 1st.!tal. Attuari 28 (1965) ARCANGELI (R.): Pseudo-solution de l'equation Ax = Y C. R. Acad. Sci. Paris.. sere A 263 (1966) ARIMOTO (S.): On a multistage nonli near programming problem. J. Math. Anal. Appl.!2. (1967) ARKIN (V.!.): On the infinite-dimensional analogue of a nonconvex programming problem (Russian). Kibernetika (Kiev) no ARMIJO (L.): Minimization of functions having Lipschitz continuous. first partial derivatives. Pacific J. Math. ~ (1966) ARROW( K. J.): Applications of control theory to economic growth. [Dantzig & Veinott ].. Part 2. pp DEBREU (G.): Existence of an equilibrium for a competitive economy. Econometrica ~ (1954) ENTHOVEN (A. C.): Quasi-concave programming. Econometrica 29 (1961) HURWICZ (L.): Reduction of constrained maxima to saddlepoint problems. Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability.. Vol. 5. pp University of California Press.. Berkeley : Gradient methods for constrained maxima. Operations Res. ~ (1957).. 258w : Gradient method for concave programming.. I: Local results. [Arrow. Hurwicz & Uzawa pp : Gradient methods for concave programming.. III: Further global results and applications to resource allocation. [Arrow.. Hurwicz & Uzawa ].. pp : Stability of the gradient process in n-person games. SIAM J. Appl. Math. ~ (1960)

15 ~ ~ UZAWA (H.): Constraint qualifications in maximization problems. Naval Res. Logist. Quart.!!. (1961)~ ~ SOLOW (R. M.): Gradient methods for constrained maxima~ with weakend assumptions. [Arrow~ Hurwicz & Uzawa~ pp ATTEIA (M.): Generalisation de la definition et des proprietes des «spline-functions». C. R. Acad. Sci. Paris 260 (1965) : Fonctions «spline» definies sur un ensemble convexe. Numer. Math. ~ (1968)~ AUMANN (R. J.)~ PERLES (M.): A variational problem arising in economics. J. Math. Anal. Appl.!,.!.(1965) AUSLENDER (A.): Algorithme de recherche des points stationnaires d'une fonctionnelle dans un espace vectoriel topologique. Application a un probleme de controle a evolution non lineaire. C. R. Acad. Sci. Paris ser. A. 266 (1968) : Methodes et tmoremes de dualite. C. R. Acad. Sci. Paris Ser. A 267 (1968) : Methodes generales pour la recherche des cols d'une fonction. C. R. Acad. Sci. Paris Ser. A 268 (1969) BRODEAU (F.): Convergence d'un algorithme de Frank et Wolfe applique a un probleme de c ontr Ole. Rev. Fran<;:aise Inform at. Recherche Operationnelle ~ (1968).. no BAKHTIN (I. A.): On an extremum problem (Russian). Z. VyCisl. Mat. i Mat. Fiz.4 (1964) USSR Comput. Math. and Math. Phys. 4 (1964).. no (English transl.) GORSTKO (A. B. ): On the solution of nonlinear extremum problems with linear constraints of specific type (Russian). [Kantorovich ].. pp KRASNO S ELSKIJ (M. A.)~ LEVIN (A. Ju. ): Finding the extremum of a function on a polyhedron (Russian). Z. Vycisl. Mat. i Mat. Fiz. 3 (l963)~ USSR Comput. Math. and Math. Phys. 3 (1963) (English transl.). -

16 BALAS (E.): Duality in discrete programming: IlL Nonlinear objective function and constraints. Management Sciences Research Report No Graduate School of Industrial Administration~ Carnegie-Mellon University~ Pittsburgh~ : Minimax et dualite en programmation discrme. Th~se Doct. ~ Universite de Paris~ BARANKIN (E. W.).. DORFMAN (R.): On quadratic programming. University of California Publications in Statistics~ Vol. 2.. pp University of California Pres.. Berkeley~ BARANOV (A. Ju. L KHOMENJUK (V. V.): Solution of the linear problem of minimization of a quadratic functional in Hilbert space (Russian). Avtomat. i Telemekh. 26 (1965L Automat. Remote Control ~ (1965)~ (English transl.). BARR (R. 0.): Computation of optimal controls by quadratic programming on convex reachable sets. Dissertation~ University of Michigan~ : Computation of optimal controls on convex reachable sets. [Balakrishnan & Neustadt~ 1967] ~ pp BARRA (J. R.)~ BENZAKEN (C. L BRODEAU (F.): Probl~mes numeriques en programmation dynamique deterministe. Rev. Fran<;aise Recherche Operationnelle ~ (1965). no. 34~ BAUMOL (W. J.)~ BUSHNELL (R. C.): Error produced by linearization in mathematical programming. Econometrica ~ (1967)~ BEALE (E. M. L.): On minimizing a convex function subject to linear inequalitie s. J. Roy. Statist. Soc. Ser. B..!2 (1955)~ : An algorithm for solving the transportation problem when the shipping cost over each route is convex. Naval Res. Logist. Quart. ~ (1959) : On quadratic programming. Naval Res. Logist. Quart. ~ (1959)~ : Note on "A comparison of two methods of quadratic programming". Operations Res. 14 (1966)~ 442-"443. : Numerical methods. [Abadie. 1967J ~ pp

17 BECKENBACH (E. F.): Convex functions. Bull. Amer. Math. Soc. 54 (1948) BECTOR (C. R.): Nonlinear indefinite functional programming with nonlinear constraints. Cahiers Centre Etudes Recherche Oper. ~ (1967)~ : Nonlinear fractional functional programming with nonlinear constraints. Z. angew. Math. Mech. 48 (1968)~ : Duality in fractional and indefinite programming. Z. angew. Math. Mech. 48 (1968)~ : Programming problems with convex fractional functions. Operations Res..!! (1968L : Indefinite cubic programming with standard errors in objective function. Unternehmensforschung g (1968)~ BEIGHTLER (C. S.)~ CRISP (R. M.)~ MEIER (W. L.): Optimization by geometric programming. J. Indust. Engrg. ~ (1968)~ ,.. WILDE (D. J.): Diagonalization of quadratic forms by Gauss elimination. Management Sci. g (1966)~ ; erratum~ ibid. g(1966)~ 908. BEJ AR ALAMO (J.): Mathematical theory of programming (Spanish). Mem. Real Acad. Ci. Exact. F!s~ Natur. Madrid ~~ no.2 (1967). BELENKIJ (V. Z.): Problems of mathematical programming having a minimum point (Russian). Dokl. Akad. Nauk SSSR 183 (l968)~ Soviet Math. Dokl. ~ (196 8)~ (English transl.). BELLMAN (R. E.): Dynamic programming and Lagrange multipliers. Proc. Nat. Acad. Sci. USA 42 (1956)~ : Dynamic programming and the numerical solution of variational problems. Operations Res. ~ (l957)~ ~ KAGIW ADA (H. H.). KALABA (R. E.): Quasilinearization~ boundary-value problems and linear programming. IEEE Trans. Automatic Control AC-10 (1965)~ 199.

18 ~ KARUSH (W.): On a new functional transform in analysis: The maximum transform Bull. Amer. Math. Soc. 22 (1961) : Mathematical programming and the maximum transform. SIAM J. Appl. Math. 1:.2. (l962)~ ~ : On the maximum transform. J. Math. Anal. Appl. ~ (l963)~ BELTRAMI (E. J.): A computational approach to necessary conditions in mathematical programming. ICC Bull. ~ (1967) On infinite - dimensional convex programs. J. Comput. System Sci. 1:. (1967) A constructive proof of the Kuhn-Tucker multiplier rule. J. Math. Anal. Appl. ~ (1969) BENDERS (J. F.): Partitioning in mathematical programming. Proefschrift~ Rijksuniversiteit te Utrecht~ : Partitioning procedures for solving mixed-variables programming problems. Numer. Math.! (1962) : Some aspects of mathematical optimization (Dutch). Euclides (Groningen) 43 (1968) BEN-ISRAEL (A.): A Newton-Raphson method for the solution of systems of equations. J. Math. Anal. Appl. ~ (l966)~ : On iterative methods for solving nonlinear least squares problems over convex sets. Israel J. Math. ~ (1967), : CHARNES (A.).. KORTANEK (K. 0.): Duality and asymptotic solvability over cones. Bull. Amer. Math. Soc. ~ (1969) BENSOUSSAN (A.).. KENNETH (P.): Sur l'analogie entre les methodes de regularisation et de penalisation. Rev. Fran<;,:aise Inform at. Recherche Operationnelle ~(1968)~ no. 13~

19 BEREANU (B.): A property of convex functions with applications to nonlinear programming (Romanian). Com. Acad. R. P. Romtne..!! (1963) : A property of convex.. piecewise linear functions with applications to mathematical programming. Unternehmensforschung ~ (1965) BERGE (C.): Sur l'equivalence du probl~me de transport generalise et du probl~me des reseaux. C. R. Acad. Sci. Paris 251 (1960) BERKOVITZ (L. D.): Variational methods in problems of control and programming. J. Math. Anal. Appl.! (1961) BERMAN (G.): Minimization by successive approximation. SIAM J. Numer. Anal.! (1966) BERNADAT (J.): Programmes quadratiques. [Fortet et al ].. pp BERNHOLTZ (B.): A new derivation of the Kuhn-Tucker conditions. Operations Res. g (1964) , BESSIERE (F.).. SAUTTER (E. A.): Optimization and suboptimization: The method of extended models in the nonlinear case. Management Sci. ~ (1968) BIGG (M. D.): The minimization of a general function subject to a set of non-linear constraints. Proc. Cambridge Philos. Soc. ~ (1963) BIRKHOFF (G.): A variational principle for nonlinear networks. Quart. Appl. Math. 3..!. (1963) DIAZ (J. B.): Nonlinear network problems. Quart. Appl. Math..!! (1956)., BffiZAK (B.).. PSHENICHNYJ (B. N.): Minimization problems for nonsmooth functions (Russian). Kibernetika (Kiev) no BITTNER (L.): Das Austauschverfahren der linearen Tschebyscheff Approximation bei nicht erfilllter Haarscher Bedingung. Z. angew. Math. Mech..!!. (1961) : Ausgleichsaufgaben der Gestalt f [max l.(x).. min 1. (x») =Min! L Wiss. Z. Techn. Univ. Dresden.!.Q (1961)

20 : Eine Verallgemeinerung des Verfahrens des logarithmischen Potentials von Frisch fur nichtlineare Optimierungsprobleme. [Prekopa~ 1965]~ pp : Begrtindung des sogenannten diskreten Maximumprinzips. Z. Wahrscheinlichkeitstheorie verw. Gebiete.!.Q (1968) : Abschatzungen bei Variationsmethoden mit Hilfe von Dualitatssatzen. I. Numer. Math.!!. (1968) BOHNENBLUST (H. F.).. KARLIN (S.).. SHAPLEY (L. S.): Games with continuous.. convex pay- off. Contributions to the Theory of Games.. Vol. 1 (H. W. Kuhn & A. W. Tucker eds.).. pp Annals of Mathematics Studies~ no. 24; Princeton University Press~ Princeton~ BONSALL (F. F.): Dual extremum problems in the theory of functions. J. London Math. Soc. ~ (1956)~ de BOOR (C.).. LYNCH (R. E.): On splines and their minimum properties. J. Math. Mech. ~ (1966) BOOT (J. C. G.): Notes on quadratic programming: The Kuhn-Tucker and Theil- van de Panne conditions.. degeneracy and equality constraints. Management Sci. ~ (1961) : On trivial and binding constraints in programming problems. Management Sci. ~ (1962) : Binding constraint procedures of quadratic programming. Econometrica ~ (1963L : On sensitivity analysis in convex quadratic programming problems Operations Res.!!. (1963) BOX (M. J.): A new method of constrained optimization and a comparison with other methods. Computer J. ~ (1965)~ : A comparison of several current optimization methods.. and the use of transformations in constrained problems. Computer J. ~ (1966) BRAESS (D.): Ueber Dampfung bei Minim ali sierungsverfahren. Computing (Arch. elektron. Rechnen) 1:. (1966) BRAM (J.): The Lagrange multiplier theorem for max-min with several constraints. SIAM J. Appl. Math.!± (1966)

21 BRANS (J. P.)~ DROESBEKE (F.): Programmes quadratiques. Cahiers Centre Etudes Recherche Oper.2. (1965)" BRATTON (D.): The duality theorem in linear programming. Cowles Commission Discussion Paper Mathematics No Cowles Commission for Re~earch in Economics6 Yale University" BREGMAN (L. M.): The method of successive projections for finding a common point of convex sets (Russian). Dokl: Akad. Nauk SSSR 162.(1965), Soviet Math. Dokl. ~ (1965), "2 (English transl.). -- : Relaxation method for finding a common point of convex sets" and its application to optimization problems (Russian). Dokl. Akad. Nauk SSSR 171 (1966)" Soviet Math. Dokl. 2. (1966)~ (English trans!.). -- : A relaxation method of finding a common point of convex sets" and its application to the solution of problems in convex programming (Russian). Z. VyCisl. Mat. i Mat. Fiz. 2. (1967)" BRIOSCHI (F.), LOCATELLI (A. F.): Extremization of constrained multi variable function: Structural programming. IEEE Trans. Systems Sci. Cybernetics SSC-3 (1967)~ 105.:-111. BRPNDSTED (A.): Conjugate convex functions in topological vector spaces. Mat. -Fys. Medd. Danske Vid. Selsk. 346 no. 2(1964). -- ~ ROCKAFELLAR (R. T.): On the subdifferentiability of convex functions. Proc. Amer. Math. Soc. ~ (1965) BROOKS (S. H.): A comparison of maximum seeking methods. Operations Res. 2. (1959), BROOKS (R.). GEOFFRION (A.): Finding Everett's Lagrange multipliers by linear programming. Operations Res. ~ (1966), BROSOWSKI (B.): Ueber Tschebyscheffsche Approximationen mit linearen Neb enb edingung en. Math. Z. 88 (1965)" : Vber Tschebyscheffsche Approximation mit verallgemeinerten rationalen Funktionen. Math. z. 90 (1965)"

22 BROWN ( G. W.): Iterative solution of games by fictitious play. [Koopmans. 1961]. pp ; von NEUMANN (J.): Solutions of games by differential equations. Contributions to the Theory of Games. Vol. 1 (H. W. Kuhn & A. W. Tucker eds.). pp Armals of Mathematics Studies. no. 24; Princeton University Press. Princeton Also in: John von Neumann. Collected Works. Vol. 6. pp Pergamon Press. Oxford BROYDEN (C. G.): A class of methods for solving nonlinear simultaneous equations. Math. Compo ~ (1965) : Quasi-Newton methods and their application to function minimization. Math. Compo ~ (1967) : A new method of solving nonlinear simultaneous equations. Computer J. g (1969) BRYSON (A. E.). DENHAM (W. F.): A steepest ascent method for solving optimum programming problems. Trans. ASME Ser. E. J. Appl. Mech. ~ (1962) DREYFUS ( S. E.): Optimal programming problems with inequality constraints. 1. AIAA J..!. (1963) BUEHLER (R. J.). SHAH (B. V.). KEMPTHORNE (0.): Methods of parallel tangents. Optimization Techniques (J. W. Blakemore & S. H. Davis eds.). PP Chemical Engineering Progress Symposium Series. no. 50; American Institute of Chemical Engineers. New York ,,- BUr - TR9NG - LIEU: On a problem of convexity and its application to non-linear stochastic programming. J. Math. Anal. Appl..!!. (1964) : A study of some inequalities for nonlinear stochastic programming. [Abadie. 1967J. pp CARTON (D.): Quelques remarques concernant les fonctions quasiconvexes. Publ. Math. Debrecen.!.!. (1964) HUARD (P.): La methode des centres dans un espace topologique. Numer. Math.!!. (1966)

23 BULAVSKLJ (V. A.)~ RUBINSHTEIN (G. Sh.): Solution of convex programming problems with linear constraints by the method of successive improvement 'of an admissible vector (Russian). Dokl. Akad. Nauk SSSR 150 (l963)~ Soviet Math. Dokl.! (l963)~ (English transl.). BURGER (E.): On extrema with side conditions. Econometrica ~ (l955)~ BUTLER (T.): Lagrange multipliers and the goemetry of Hilbert space. SIAM J. Appl. Math. g (l964)~ ~ MARTIN (A. V.): On a method of Courant for minimizing functionals. J. Math. and Phys.!!. (1962)~ BUTZ (A. P.): Iterative saddle point techniques. SIAM J. Appl. Math. ~ (1967)~ CAMION (P.): Application d'une generalisation du lemme de Minty ~ un probleme d'injimum de fonction convexe. Cahiers Centre Etudes Recherche Oper. 7 (1965)~ ; erratum~ ibid. ~ (1966)~ CAMP (G. D.): Inequality-constrained stationary value problems. Operations Res. ~ (l955)~ CANDLER (W.)~ TOWNSLEY (R. J.): The maximization of a quadratic function of variables subject to linear inequalities. Management Sci.!.Q (1964)~ CANNON (R. J.): The numerical solution of the Dirichlet problem for Laplace's equation by linear programming. SIAM J. Appl. Math. g (1964)~ ~ CECCHI (M. M.): The numerical solution of some biharmonic problems by mathematical programming techniques. SIAM J. Numer. Anal. ~ (l966)~ ~ --- : Numerical experiments on the solution of some biharmonic problems by mathematical programming techniques. SIAM J. Numer. Anal.! (1967)~ CANON (M. D.): A new algorithm for bounded variable quadratic programming problems. Dissertation~ University of California~ Berkeley~ : Mathematical programming and discrete optimal control. IBM Research Report RC IBM Research Center~ Yorktown Heights N. Y. ~ 1968.

24 : Monoextremal representations of a class of minimax problems. Management Sci. ~ (1969)~ ~ CULLUM (C. D. ),: A tight upper bound on the rate of convergence of the Frank-Wolfe algorithm. SIAM J. Control ~ (1968)~ ~ --- : The determination of optimum separating hyperplanes. L A finite step procedure. IBM Research Report RC IBM Research Center~ Yorktown Heights~ N. Y. ~ ~ --- ~ POLAK (E.): Constrained minimization problems in finite-dimensional spaces. SIAM J. Control! (1966)~ ~ EATON (J. H.): A new algorithm for a class of quadratic programming problems~ with application to control. SIAM J. Control! (1966)~ CARPENTIER (J.)~ ABADIE (J.): Gemeralisation de la methode du gradient reduit de Wolfe au cas de contraintes non line aires. In: Proceedings of the 4th International Conference on Operational Research (Boston 1966). Wiley~ New York (to appear). CARROLL (C. W.): The created response surface technique for optimizing nonlinear restrained systems. Operations Res.!!. (1961)~ CAR TER (I. P. V.): Optimization techniques. Nordisk Tidskr. Informations-Behandling ~ (1963)~ CAUCHY (A.): Methode generale pour la resolution des syst~mes d'equations simultanees. C. R. Acad. Sci. Paris 25 (1847)~ Also in: OEuvres complmes d' Augustin Cauchy~ Tome X~ pp Gauthier-Villars. Paris~ 1901., CEA (J.): Les methodes de "descente" dans la theorie de l'optimisation. Rev. Franc;aise Informat. Recherche Operationnelle ~ (1968)~ no. 13~ CHADDA ( S. S.): A decomposition principle for fractional programming. Opsearch (India)! (l967)~ no. 3~ CHANDRA (S.): The capacitated transportation preblem in linear fractional functional programming. J. Operations Res. Soc. Japan.!.Q. (1967L

25 : Decomposition principle for linear fractional functional programs. Rev. Fran<;:aise Inform at. Recherche Operationnelle ~ (1968)" no. 10" CHARNES (A.): The geometry of convergence of simple perceptrons. J. Math. Anal. Appl. J.. (1963) : Some fundamental theorems of perceptron theory and their geometry. Computer and Information Sciences (J. T. Tou & R. H. Wilcox eds. L pp Spartan Books.. Washington CLOWER (R. W.).. KORTANEK (K.): Effective control through coherent decentralization with preemptive goals. Econometrica ~ (1967) COOPER (W. W.): Nonlinear power of adjacent extreme point methods of linear programming. Econometrica ~ (1957) : Nonlinear network flows and convex programming over incidence matrices. Naval Res. Logist. Quart. ~ (1958) : Programming with linear fractional functionals. Naval Res. Logist. Quart. ~ (1962) : Deterministic equivalents for optimizing and satisficing under chance constraints. Operations Res..!:l (1963) : Optimizing engineering designs under inequality constraints. Cahiers Centre Etudes Recherche Oper. ~ (1964) : A note on the 'fail-safe' properties of the "generalized Lagrange multiplier method". Operations Res. II (1965) : A convex approximant method for noneonvex extensions of geometric programming. Proc. Nat. Acad. Sci. USA ~ (1966) KOR T ANEK (K. 0.): Duality.. Haar programs.. and finite sequence spaces. Proc. Nat. Acad. Sci. USA 48 (1962) A duality theory for convex programs with convex constraints. Bull. Amer. Math. Soc. 68 (1962)

26 ~ ~ --- : Duality in semi-infinite programs and some works of Haar and Caratheodory. Management Sci. 9 (1963)~ ; erratum~ ibid. ~ (1963) ~ --- ~ --- : Duality in semi-infinite programming and some works of Haar and, Caratheodory. Proceedings of the 3rd International Conference on Operational Research (Oslo 1963)~ pp Dunod~ Paris~ ~ --- ~ --- : On representations of semi-infinite programs which have no duality gaps. Management Sci. ~ (1965) ~ --- ~ --- : Semi-infinite programming~ differentiability and geometric programming. II. Aplikace Mat.!! (1969)~ ~ --- ~ --- : On the theory of semi-infinite programming and a generalization of the Kuhn- Tucker saddle point theorem for arbitrary convex functions. Naval Res. Logist. Quart. ~ (1969)~ ~ FIACCO (A. V.)~ LITTLECHILD (S. C.): Convex approximants and decentralization: A SUMT approach. Systems Research Memorandum No The Technological Institute~ Northwestern University~ Evanston, ~ KIRBY (M.): Modular design~ generalized inverses and convex programming. Operations Res. ~ (1965)~ ~ KOR T ANEK (K. 0.): A generalization of a theorem of Edmund Eisenberg. Systems Research Memorandum No The Technological Institute~ Northwestern University. Evanston~ ~ : A note on the discrete maximum principle and distribution problems. J. Math. and Phys. 45 (1966)~ ~ LEMKE (C. E.): Minimization of non-linear separable convex functionals. Naval Res. Logist. Quart. 1:. (1954)~ CHAZAN (D.): A new proof of a min-max theorem. IBM Research Report RC IBM Research Center~ Heights~ N. Y Yorktown

27 : Profit functions and optimal control: an alternate description of the control problem. J. Math. Anal. Appl. ~ (1968) MIRANKER (W. L.): A non-gradient and parallel algorithm for unconstrained minimization. IBM Research Report RC IBM Research Center.. Yorktown.. Heights N. Y CHENERY (H. B.).. UZAWA (H.): Non-linear programming in economic development. [Arrow.. Hurwiez & Uzawa ].. pp CHENEY (E. W.).. GOLDSTEIN (A. A.): NeWton's method for convex programming and Tchebycheff approximation. Numer. Math..!.. (1959) : Proximity maps for convex sets. Proc. Amer. Math. Soc..!..Q (1959), : Tchebycheff approximation in locally convex spaces. Bull. Amer. Math. Soc. 68 (1962), : Tchebychefi approximation and related extremal problems. J. Math. Mech. 14 (1965) LOEB (H. L.): Two new algorithms for rational approximation. Numer. Math. ~ (1961), : On rational Chebyshev approximation. Numer. Math. i (1962) CHERRUAULT (Y. ): Une methode directe de minimisation et applications. Rev. Franc;aise Informat. Recherche Operationnelle ~ (1968).. no CHOW (W. M.): A note on the calculation of certain constrained maxima. Technometrics i (1962) CLIMESCU (A.): Algebraic programming. I. II.. III.. IV. Bul. Inst. Politehn. Iasi (N. S.) 8 (1962).. no (Romanian),; 8 (1962). no (French); 10 (1964). no (French). 11 (1965).. no (Romanian). COLLATZ (L.): Tschebyscheffsche Approximation. Randwertaufgaben und Optimierungsaufgaben. Wiss. Z. Hochsch. Architektur Bauwesen Weimar g (1965),

28 : Lineare Randwertaufgaben und Approximationen von Funktionen. Mathematica (Cluj).!.Q (1968) : Zur mimerischen Behandlung der rationalen Tschebyscheff Approximation bei mehreren unabhangigen Veranderlichen. Aplikace Mat. ~ (1968) COLVILLE (A. R.): A comparative study of nonlinear programming codes. Technical Report No IBM New York Scientific Center l New York l COROIU (R.): Simplex methods for solving quadratic programming problems. Econom. Comput. Econom. Cybernetics Stud. Res. (Bucharest) no COTTLE (R. W.): A theorem of Fritz John in mathematical programming. RAND-Report RM PRo The RAND Corp. 1 Santa Monica.. Calif : Formal self-duality in nonlinear programming. Report ORC pp Operations Research Center l University of California.. Berkeley : An infinite game with a convex-concave payoff kernel. Report ORC pp Operations Research Center.. University of California. Berkeley : Symmetric dual quadratic programs. Quart. Appl. Math. ~ (1963) : Note on a fundamental theorem in quadratic programming. SIAM J. Appl. Math. ~ (1964) : Nonlinear programs with positively bounded Jacobians. SIAM J. Appl. Math.!i (1966) : On the convexity of quadratic forms over convex sets. Operations Res. ~ (1967) : Comments on the note by Kortanek and Jeroslow. Operations Res. ~ (1967) : The principal pivoting method of quadratic programming. [Dantzig & Veinott l 1968] 1 Part 11 pp : On a problem in linear inequalities. J. London Math. Soc. 43 (1968)

29 DANTZIG (G. B.): Complementary pivot theory of mathematical programming. Linear Algebra and Appl.!. (1968) II : Complementary pivot theory of mathematical programming. [Dantzig & Veinott ].. Part 1.. pp II MOND (B.): Self-duality in mathematical programming. SIAM J. Appl. Math.!! (1966) CROCKETT (J. B.).. CHERNOFF (H.): Gradient methods of maximization. Pacific J. Math.E. (1955) CULLEN (D. E.): Solving nonlinear inequalties by relaxation.. with applications to nonlinear programming. Dissertation.. Washington University CURRY (H. B.): The method of steepest descent for nonlinear minimization problems. Quart. Appl. Math. ~ (1944L CURTIS (A. R.).. POWELL (M. J. D.): Necessary conditions for minimax approximation. Computer J. ~ (1965) : On the convergence of exchange algorithms for calculating minim ax-approximations. Computer J. ~ (1966) CURTIS (P. C.).. FRANK (W. L.): An algorithm for the determination of the polynomial of best minimax approximation to a function defined on a finite point set. J. Assoc. Comput. Mach. ~ (1959) DA CUNHA (N. 0.).. POLAK (E.): Constrained minimization under vector valued criteria in finite dimensional spaces. J. Math. Anal. Appl.!2. (1967) '" --- : Constrained minimization under vector-valued criteria in linear topological spaces. [Balakrishnan & Neustadt", 1967J.. pp DANIEL (J. W.): The conjugate gradient method for linear and nonlinear operator equations. SIAM J. Numer. Anal.! (1967) DANSKIN(J. M.): Fictitious play for continuous games. Naval Res. Logist. Quart.!. (1954)

30 : The theory of min-max~ with applications. SIAM J. Appl. Math. 14 (l966)~ : Note on the sequential maximization technique. Operations Res. ~ (l967)~ : On suboptimization : an example. Operations Res. ~ (l968)~ DANTZIG (G. B.): A proof of the equivalence of the programming problem and the game problem. rkoopmans~ 1951] ~ pp : Maximization of a linear function of variables subject to linear inequalities. [Koopmans~ 1951J ~ pp : Note on B. Klein's IIDirect use of extremal principles in solving certain optimizing problems involving inequalities ll Operations Res. ± (1956)~ : General convex objective forms. Mathematical Methods in the Social Sciences~ S. Karlin & P. Suppes eds.)~ pp Stanford University Press~ Stanford~ (K. J. Arrow~ --- : Quadratic programming. A variant of the Wolfe-Markowitz algorithms. Report ORC Operations Research Center. University of California.. Berkeley : Optimization in Operations Research. Information Processing 1965 (Proceedings of IFIP Congress 65).. Vol. 1.. pp Spartan Books.. Washington D. C : Linear control processes and mathematical programming. SIAM J. Control 4 (1966) Also in: [Dantzig -& Veinott L Part 2.. pp : Application of generalized linear programming to control theory. [Ahadie~ 1967J.. pp COTTLE (R. W.): Positive (semi-) definite programming. rabadie ].. pp EISENBERG (E.)~ COTTLE(R. W.): Symmetric dual nonlinear programs. Pacific J. Math. ~ (1965)~

31 ~ FOLKMAN (J.)~ SHAPIRO (N.): On the continuity of the minimum set of a continuous function. J. Math. Anal. Appl.!1. (l967)~ ~ FORD (L. R.)~ FULKERSON (D. R.): A primal-dual algorithm for linear programs. [Kuhn & Tucker~ 1956] ~ pp ~ ORDEN (A.)~ WOLFE (Ph.): The generalized simplex method for minimizing a linear form under linear inequality restraints. Pacific J. Math. ~ (1955)~ ~ V AN SL YKE (R. M.): Generalized upper bounding techniques. J. Comput. System Sci.! (1967)~ ~ WALD (A.): On the fundamental lemma of Neyman and Pearson. Ann. Math. Statist. 22 (1951)~ ~ WOLFE (Ph.): Decomposition principle for linear programs. Operations Res. ~ (1960)~ ~ -- : The decomposition algorithm for linear programs. Econometrica ~ (1961L DAVID ON (W. C.): Var~able metric method for minimization. Atomic Energy Commission Report ANL Argonne National Laboratory~ Lemont~ ill. # : Variance algorithm for minimization. Computer J.!Q (1968L DAVIS (P. J.)~ WILSON (M. W.): Non-negative interpolation formulas for uniformly elliptic equations. IBM Research Report RC IBM Research Center# Yorktown Heights~ N. Y. ~ DAVYDOV (E. G.): Application of Stieltjes moments (Russian). Z. Vycisl. Mat. i Mat. Fiz. J.. (1967)~ DEBREU (G. E.): Definite and semidefinite quadratic forms. Econometrica 20 (l952)~ : Economic equilibrium. Mat hematical Systems Theory and Economics I (H. W. Kuhn & G. P. Szeg6 eds.)~ pp Springer~ Berlin~ DEJON (B.)~ NICKEL (K.): A never failing~ fast converging rootfinding algorithm. Constructive Aspects of the Fundamental Theorem of Algebra (B. Dejon & p. Henrici eds.)~ pp Wiley~ New York~ 1969.

32 DEMJ ANOV (V. F.): Solution of certain extremal problems (Russian). Avtomat. i Tel em ekh. 26 (1965)~ Automat. Remote Control 26 (1965)~ (English transl.). --- : Minimization of functions on convex bounded sets (Russian). Kibernetika (Kiev) 1965~ no Cybernetics 1:. (1965) no (English transl.). --- : On minimization of the maximal deviation (Russian). Vestnik Leningrad. Univ. ~ (1966)~ no. 7~ : On the solution of certain minimax problems. I~ II (Russian). Kibernetika (Kiev) 1966~ no. 6~ 58-66; 1967~ no : Successive approximations for finding saddle points (Russian). Dokl. Akad. Nauk SSSR 177 (1967) Soviet Math. Dokl. ~ (1967)~ (English transl.). --- : The investigation of saddle points (Russian). Vestnik Leningrad. Univ. ~ (1967). no : The directional derivative of a maximin function (Russian). Dokl. Akad. Nauk SSSR 179 (1968) : The use of second derivatives in the minimization of functions on bounded sets (Russian). Vestnik Leningrad. Univ. ~ (1968). no Algorithms for some minimax problems. J. Comput. System Sci. ~ (1968) , : Differentiation.., of the maximin function. I. II (Russian). Z. Vycisl. Mat. i Mat. Fiz.... (1968) ; ~ (1969), RUBINOV (A. M.): The minimization of a smooth convex functional on a convex set (Russian). Vestnik Leningrad. Univ. 19 (1964). no. 4~ SIAM J. Control ~ (1967) (English transl.) : On the problem of minimization of a smooth functional with convex constraints (Russian). Dokl. Akad. Nauk SSSR 160 (1965) Soviet Math. Dokl. ~ (1965) (English transl.).... : On necessary conditions for an extremum (Russian). Ekonom. i Mat. Metody ~ (1966)~ : Minimization of functionals in normed spaces. SIAM J. Control ~ (1968)

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