Anhang. Bibliographie zur Nichtlinearen Programmierung

Transcription

1 Anhang Bibliographie zur Nichtlinearen Programmierung

2 Bibliographie 333 A. Lehrbucher und Monographien ADBY (P.R.), DEMPSTER (M.A. H.) : Introduction to Optimization Methods. Chapman and Hall, London, AOKI (M.): Introduction to Optimization Techniques. Macmillan, New York, 1971 ARROW (K.J.), HAHN (F.H.): General Competitive Analysis. Holden-Day, San Francisco, AUSLENDER (A.): Problemes de Minimax via 1 'Analyse Convexe et les Inega- 1 ites Variationnel les: Theorie et Algorithmes (Lecture Notes in Economics and Mathematical Systems, 77). Springer, Berl in, BALAKRISHNAN (A.V.): Introduction to Optimization Theory in a Hilbert Space (Lecture Notes in Operations Research and Mathematical Systems, 42). Springer, Ber! in, BELTRAMI (LJ.): An Algorithmic Approach to Nonl inear Analysis and Optimization. Academic Press, New York, BERGE (C.): Espaces topologiques, fonctions multivoques (deuxieme edition). Dunod, Paris, BERGE (C.), GHOUl LA-HOURI Dunod, Paris, (A.): Programmes, jeux et reseaux de transport. BERMAN (A.): Cones, Matrices and Mathematical Programming (Lecture Notes in Economics and Mathematical Systems, 79). Springer, Berlin, BOOT (J.C.G.): Quadratic Programming. North-Holland, Amsterdam, BOX (M.J.), DAVIES (D.), SWANN (W.H.): Non-Linear Optimization Techniques. 01 iver and Boyd,. Edinburgh, BRACKEN (J.), McCORMICK (G.P.): Selected Appl ications of Nonl inear Programming. Wiley, New York, BRENT (R.P.): Algorithms for Minimization without Derivatives. Prentice Hall, Englewood Cliffs, CANON (M.D.), CULLUM (C.D.), POLAK (E.): Theory of Optimal Control and Mathematical Programming. McGraw-Hill, New York, CEA (J.): Optimisation: theorie et algorithmes. Dunod, Paris, COLLATZ (L.), WETTERLING (W.): Optimierungsaufgaben (2. Auflage). Springer, Ber! in, DANIEL (J.W.): The Approximate Minimization of Functionals. Prentice-Hall, Englewood Cl i ffs, N.J., DANSKIN (J.M.): The Theory of Max-Min. Springer, Berlin, DANTZIG (G.B.): Linear Programming and Extensions. Princeton University Press, Princeton, DEMYANOV (V.F.), MALOZEMOV (V.N.): Introduction to Minimax. Wiley, NewYork,1974. DEMYANOV (V. F.), RUBINOV (A.M.): Approximate Methods in Optimization Problems. American Elsevier, New York, DENNIS (J.B.): Mathematical Programming and Electrical Networks. Wiley, New York, 1959.

3 334 Bibliographie DIXON (L.C.W.): Nonl inear Optimisation. The Engl ish Universities Press, London, DUFFIN (R.J.), PETERSON (E.L.), ZENER (C.): Geometric Programming. Wiley, New York, EGGLESTON (H.G.): Convexity. Cambridge University Press, Cambridge, EKELAND (I.), TEMAM (R.): Analyse convexe et problemes variationnels. Dunod, Paris, EL-HODIRI (M.A.): Constrained Extrema. Introduction to the Differentiable Case with Economic Appl ications (Lecture Notes in Operations Research and Mathematical Systems, 56). Springer, Berl in, FIACCO (A.V.), McCORMICK (G.P.): Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York, FR~NKEL (H.): Diskrete optimale Steuerungsprobleme und konvexe Optimierung. Walter de Gruyter, Berl in, GIRSANOV (I.V.): Lectures on Mathematical Theory of Extremum Problems (Lecture Notes in Economics and Mathematical Systems, 67). Springer, Be r lin, GOLDSTEIN (A.A.): Constructive Real Analysis. Harper & Row, New York, GOLSTEIN (E.G.): Theory of Convex Programming (Translations of Mathematical Monographs, Vol.36). American Mathematical Society, Providence, R.I., GoPFERT (A.): Mathematische Optimierung in allgemeinen Vektorraumen. B.G. Teubner, Leipzig, HADLEY (G.): Nonl inear and Dynamic Programming. Addison-Wesley, Reading, Mass., HESTENES (M.R.): Calculus of Variations and Optimal Control Theory. Wiley, New York, HIMMELBLAU (D.M.): Appl ied Nonl inear Programming. McGraw-Hili, New York, HOLMES (R.B.): A Course on Optimization and Best Approximation (Lecture Notes in Mathematics, 257). Springer, Berl in, INTRILIGATOR (M.D.): Mathematical Optimization and Economic Theory. Prentice-Hal I, Englewood CI iffs, N.J., JACOBY (S.L.S.), KOWALIK (J.S.), PIZZO (J.T.): Iterative Methods for Nonlinear Optimization Problems. Prentice-Hal I, Englewood CI iffs, N.J., KARLIN (S.): Mathematical Methods and Theory in Games, Programming, and Economics, 2 Vols. Addison-Wesley, Reading, Mass., KOWALIK (J.), OSBORNE (M.R.): Methods for Unconstrained Optimization Problems. American Elsevier, New York, KUNZI (H.P.), KRELLE (W.): Nichtl ineare Programmierung. Springer, Berl in, KUNZI (H.P.), OETTLI (W.): Nichtl ineare Optimierung: Neuere Verfahren, Bib- I iographie. (Lecture Notes in Operations Research and Mathematical Systems, 16). Springer, Berl in, KUNZI (H.P.), TZSCHACH (H.G.), ZEHNDER (C.A.): Numerische Methoden der mathematischen Optimierung. B.G. Teubner, Stuttgart, 1967.

4 Bibliographie 335 LASDON (L.S.): Optimization Theory for Large Systems. Macmil lan, New York, LAURENT (P.-J.): Approximation et optimisation. Hermann, Paris, LUENBERGER (D.G.): Optimization by Vector Space Methods. Wiley, New York, LUENBERGER (D.G.): Introduction to Linear and Nonl inear Programming. Addison-Wesley, Reading, Mass., MANGASARIAN (O.L.): Nonl inear Programming. McGraw-Hill, New York, NEUSTADT (L.W.): Optimization. Princeton University Press, Princeton, NIKAIDO (H.): Convex Structures and Economic Theory. Academic Press, New York, POLAK (E.): Computational Methods in Optimization. Academic Press, New York, PSHENICHNYI (B.N.): Necessary Conditions for an Extremum. Marcel Dekker, New York, ROBERTS (A.W.), VARBERG (D.E.): Convex Functions. Academic Press, New York, ROCKAFELLAR (R.T.): Convex Analysis. Princeton University Press, Princeton, ROCKAFELLAR (R.T.): Conjugate Dual ity and Optimization. Society for Industrial and Appl ied Mathematics, Philadelphia, RUSSEL (D.L.): Optimization Theory. W.A. Benjamin, New York, SANDER (H.-J.): Dual itat bei Optimierungsaufgaben. R. Oldenbourg, MUnchen, SCARF (H.), HANSEN (T.): The Computation of Economic Equil ibria. Yale University Press, New Haven, STOER (J.), WITZGALL (C.): Convexity and Optimization in Finite Dimensions. I. Springer, Berl in, SUCHOWITZKI (S.I.), AWDEJEWA (L.I.): Lineare und konvexe Programmierung. R. Oldenbourg, MUnchen, TABAK (D.), KUO (B.C.): Optimal Control by Mathematical Programming. Prentice-Hall, Englewood Cl iffs, VAJDA (S.): Mathematical Programming. Addison-Wesley, Reading, Mass., VAJDA (S.): Theory of Linear and Non-Linear Programming. Longman, London, VALENTINE (F.A.): Convex Sets. McGraw-Hi 1 1, New York, VAN DE PANNE (C.): Methods for Linear and Quadratic Programming. North Holland, Amsterdam, VARAIYA (P.P.): Notes on Optimization. Van Nostrand Reinhold, New York, WHITTLE (P.): Optimization under Constraints. Wiley-Interscience, London, WILDE (D.J.): Optimum Seeking Methods. Prentice-Hal I, Englewood Cl iffs, N. J., WILDE (D.J.), BEIGHTLER (C.S.): Foundations of Optimization. Prentice Ha 11, Eng 1 ewood eli f f s, N. J., 1964.

5 336 Bibliographie ZANGWILL (W. I.): Nonl inear Programming. Prentice-Hall, Englewood Cl iffs, N. J., ZOUTENDIJK (G.): Methods of Feasible Directions. Elsevier, Amsterdam, B. Sammelbande ABADIE (J.), ed.: Nonl inear Programming. North-Holland, Amsterdam, ABADIE (J.), ed.: Integer and Nonl inear Programming. North-Holland, Amsterdam, ANDERSSEN (R.S.), JENNINGS (L.S.), RYAN (D.M.), eds.: Optimization. University of Queensland Press, St. Lucia, Queensland, ARROW (K.J.), HURWICZ (L.), UZAWA (H.), eds.: Studies in Linear and Non- 1 inear Programming. Stanford University Press, Stanford, AVRIEL (M.), RIJCKAERT (M.J.), WILDE (D.J.), eds.: Optimization and Design. Prentice-Hall, Englewood Cl iffs, N.J., BALAKRISHNAN (A.V.), ed.: Techniques of Optimization. Academic Press, New York, BALAKRISHNAN (A.V.), NEUSTADT (L.W.), eds.: Mathematical Theory of Control. Academic Press, New York, BEALE (E.M.L.), ed.: Appl ications of Mathematical Programming Techniques. Engl ish Universities Press, London, BELLMAN (R.), ed.: Mathematical Optimization Techniques. University of Cal i fornia Press, Berkeley, BROISE (P.), HUARD (P.), SENTENAC (J.): Decomposition des programmes mathematiques (Monographies de recherche operationnelle, 6). Dunod, Paris, COLLATZ (L.), WETTERLING (W.), Hrsg.: Numerische Methoden bei Optimierungsaufgaben (ISNM, Vo1.1n. Birkhauser, Basel, CONTI (R.), RUBERTI (A.), eds.: 5th Conference on Optimization Techniques, Part I (Lecture Notes in Computer Science, 3): Springer, Berl in, DANTZIG (G.B.), VEINOTT (A.F.), eds.: Mathematics of the Decision Sciences, Part 1,2 (Lectures in Appl ied Mathematics, Vol. 11, 12). American Mathematical Society, Providence, R. I., FLETCHER (R.), ed.: Optimization. Academic Press, London, FORTET (R.), et al.: Mathematique des programmes economiques (Monographies de recherche operationnel Ie, I). Dunod, Paris, GEOFFRION (A.M.), ed.: Perspectives on Optimization. Addison-Wesley, Reading, Mass., GHIZZETTI (A.), ed.: Theory and Appl ications of Monotone Operators (Proceedings of a NATO Advanced Study Institute, Venice). Edizioni Oderisi, Gubbio, GRAVES (R.L.), WOLFE (P.), eds.: Recent Advances in Mathematical Programming. McGraw-Hi 1 1, New York, HIMMELBLAU (D.M.), ed.: Decomposition of Large-Scale Problems. North-Holland, Amsterdam, KOOPMANS (T.C.), ed.: Activity Analysis of Production and Allocation. Wiley, New York, KUHN (H.W.), ed.: Proceedings of the Princeton Symposium on Mathematical Programming. Princeton University Press, Princeton, 1970.

6 Bibliographie 337 KUHN (H.W.), SZEGo (G.P.), eds.: Differential Games and Related Topics. North Hoi land, Amsterdam, KUHN (H.W.), TUCKER (A.W.), eds.: Linear Inequal ities and Related Systems (Annals of Mathematics Studies, no.3~). Princeton University Press, Princeton, LAVI (A.), VOGL (T.P.), eds.: Recent Advances in Optimization Techniques. Wiley, New York, LOOTSMA (F.A.), ed.: Numerical 11ethods for Non-l inear Optimization. Academic Press, New York, ~O! (J.), ~O~ (M.W.), eds.: Mathematical Models in Economics. North-Holland, Amsterdam, VAN MOESEKE (P.), ed.: Mathematical Programs for Activity Analysis. North Holland, Amsterdam, MURRAY (W.), ed.: Numerical Methods for Unconstrained Optimization. Academic Press, London, PREKOPA (A.), ed.: Colloquium on Appl ications of Mathematics to Economics. Akademiai Kiadb, Budapest, ROSEN (J.B.), MANGASARIAN (O.L.), RITTER (K.), eds.: Nonl inear Programming. Academic Press, New York, SZEGo (G.P.), ed.: Minimization Algorithms. Mathematical Theories and Computer Results. Academic Press, New York, ZADEH (L.A.), NEUSTADT (L.W.), BALAKRISHNAN (A.V.), eds.: Computing Methods in Optimization Problems - 2. Academic Press, New York, c. Aufsatze *) ABADIE (J.): Programmation mathematique. Actes du 5eme Congres AFIRO, pp Association Fransaise d' Informatique et de Recherche Operationnel Ie, Paris, : On the Kuhn-Tucker theorem. [Abadie, 1967l, pp : Appl ication of the GRG algorithm to optimal control problems. [Abadie, 1970l, pp : Simplex-l ike methods for non-l inear programming. [Szego, 1972l, pp , CARPENTIER (J.): Generalization of the Wolfe reduced gradient method to the case of nonl inear constraints. [Fletcher, 1969], pp ABLOW (C.M.), BRIGHAM (G.): An analog solution of programming problems. Operations Res. 1 (1955), ABRAMS (R.A.): Nonl inear Programming in complex space: Sufficient conditions and dual ity. J. Math. Anal. Appl. ~ (1972), , BEN-ISRAEL (A.): A dual ity theorem for complex quadratic programming. J. Optimization Theory Appl. ~ (1969), , --: Nonl inear programming in complex space: Necessary conditions. SIAM J. Control 1 (1971), ABRHAM (J.): An approximate method for convex programming. Econometrica ~ (1961), *) Auf die im Abschnitt B aufgefohrten Sammelbande wird durch Angabe von Herausgeber und Erscheinungsjahr verwiesen. Die for die Zeitschriften verwendeten AbkOrzungen folgen dem Stil der "Mathematical Reviews".

7 338 Bibliographie --: The multiplex method and its appl ication to concave programming. Czechoslovak Math. J. ~ (1962), , ARRI (P.S.): Approximation of separable functions in convex programming. INFOR - Canad. J. Operational Res. and Information Processing ~ (1973), ADACHI (N.): On variable-metric algorithms. J. Optimization Theory Appl. I (1971), AFRIAT (S.N.): The progressive support method for convex programming. SIAM J. Numer. Anal. I (1970), : Theory of maxima and the method of Lagrange. SIAM J. Appl. Math. 20 (1971), : The output I imit function in general and convex programming and the theory of production. Econometrica 12 (1971), AGGARWAL (S.P.): A note on quasiconvex programming. Metrika ~ (1968), AGMON (S.): The relaxation method for linear inequal ities. Canad. J. Math. 6 (1954), ALLRAN (R.R.), JOHNSEN (S.E.J.): An algorithm for solving nonl inear programming problems subject to nonl inear inequal ity constraints. Computer J. ~ (1970), ALTMAN (M.): Stationary points in non-i inear programming. Bull. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. ~ (1964), : A feasible direction method for solving the nonl inear programming problem. Bull. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. ~ (1964), : A general ized gradient method for the conditional minimum of a functional. Bull. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. ~ (1966), : A general ized gradient method with self-fixing step size for the conditional minimum of a functional. Bul I. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. ~ (19671, : A general ized gradient method for the conditional extremum of a function. Bull. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. ~ (1967), : Bilinear Programming. Bull. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. ~ (1968), : A general maximum principle for optimization problems. Studia Math. ~ (1968), : A general ized gradient method of minimizing a functional on a non-l inear surface, with appl ication to non-l inear programming. Mathematica (Cluj) ~ (1969), : Theoreme general de separation des appl ications. Dual ite dans la programmation mathematique. Fonctions duales. C.R. Acad. Sci. Paris Ser. A 269 (1969), : A general separation theorem for mappings, saddle-points, dual ity, and conjugate functions. Studia Math. 36 (1970), : A general maximum principle for optimization problems with operator inequalities. Boll. Unione Mat. Ital.!: (1970), ANDREEV (N. I.): A method of solution of certain problems in non-i inear programming (Russian). Izv. Akad. Nauk SSSR Tekhn. Kibernet. 1963, no. 1, ARIMOTO (S.): On a multistage nonl inear programming problem. J. Math. Anal. Appl. Jl (196 7J, ARMACOST (R.L.), FIACCO (A.V.): Computational experience in sensitivity analysis for nonl inear programming. Math. Programming ~ (1974),

8 Bibliographie 339 ARMIJO (L.): Minimization of functions having Lipschitz continuous first partial derivatives. Pacific J. Math. ~ (1966), 1-3. ARROW (K.J.), ENTHOVEN (A.C.): Quasi-concave programming. Econometrica 29 (1961), , GOULD (F.J.), HOWE (S.M.): A general saddle point result for constrained optimization. Math. Programming 2 (1973), , HURWICZ (L.): Reduction of constrained maxima to saddle-point problems. Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability, Vol. 5, pp University of California Press, Berkeley, 1956., Gradient methods for constrained maxima. Operations Res. 2 (1957), , Gradient method for concave programming. I, III. [Arrow, Hurwicz, Uzawa, 1958], pp ; pp , -----, UZAWA (H.): Constraint qualifications in maximization problems. Naval Res. Logist. Quart.! (1961), , SOLOW (R.M.): Gradient methods for constrained maxima, with weakened assumptions. [Arrow, Hurwicz, Uzawa, 1958], pp ARSENE (C.), SBURLAN (S.): A method for the approximate solving of some limit problems based on the quadratic programming. Rev. Roumaine Math. Pures Appl...!i (1970), ASAADI (J.): A computational comparison of some non-l inear programs. Math. Programming ~ (1973), ASTAFEV (N.N.): On the direct and the inverse dual ity theorem in convex programming (Russian). Optimal. Planirovanie ~ (1969), : On general ized inverse dual ity theorems in convex programming problems (Russian). Dokl. Akad. Nauk SSSR 199 (1971), Soviet ~lath. Dokl. 12 (1971), (Engl ish transit - ATHANS (M.), GEERING (H.P.): Necessary and sufficient conditions for differentiable nonscalar-valued functions to attain extrema. IEEE Trans. Automatic Control AC-18 (1973), AUBIN (J.-P.): Characterization of the sets of constraints for which the necessary conditions for optimization problems hold. SIAM J. Control! (1970), 14ti : A Pareto minimum principle. [Kuhn, Szego, 1971l, pp : Theoreme du minimax pour une classe de fonctions. C.R. Acad. Sci. Paris Ser. A 274 (1972), : Multipl icateurs de Kuhn-Tucker pour des jeux non cooperatifs contraints. Ann. Scuola Norm. Sup. Pisa '!:l. (1973), , MOULIN (H.): Condition necessaire et suffisante d'existence d'une solution du probleme dual d'un probleme d'optimisation. C.R. Acad. Sci. Paris Ser. A 274 (1972), AUSLENDER (A.): Methodes du second ordre dans les problemes d'optimisation avec contraintes. Rev. Franjaise Informat. Recherche Operationnelle 1 (1969), no. R-2, : Recherche des points de selle d'une fonction. Symposium on Optimization (Lecture Notes in Mathematics, 132), pp Springer, Berl in, : Recherche des points de selle d'une fonction. Cahiers Centre Etudes Recherche Oper. ~ (1970), : Methodes et theoremes de dua lite. Rev. Frania i se I nformat. Recherche Operationnelle ~ (1970), no. 1, 9-45.

9 340 Bibliographie --: Methodes numer'ques pour la decomposition et la minimisation de fonctions non differentiables. Numer. Math. ~ (1971), : Une methodes generale pour la resolution et la decomposition de problemes de cols avec contraintes. C.R. Acad. Sci. Paris Ser. A 272 (1971), : Une methode de reso I ut i on des prob I emes de co I. Rev. Fran1a i se Automat. Informat. Recherche Operationnelle I (1973), no. R-l, : Resolution numerique d'inegalites variationnelles. Rev. Franiaise Automat. Informat. Recherche Operationnel Ie I (1973), no. R-2, , GOURGAND (M.), GUILLET (A.): Resolution numerique d' inegal ites variationnelles. Analyse convexe et ses appl ications (Lecture Notes in Economics and Mathematical Systems, 102), pp Springer, Berl in, , MARTINET (B.): Methodes de decomposition pour la minimisation d'une fonctionnelle sur un espace produit. C.R. Acad. Sci. Paris Ser. A 274 (1972), AVDEEVA (L. I.): Appl ication of convex programming methods to the solution of Chebyshev approximation problems (Russian). Kibernetika (Kiev) 1969, no. 3, AVRIEL (M.): Fundamentals of geometric programming. [Beale, 1970], pp r-convex functions. Math. Programming ~ (1972), Solution of certain nonl inear programs involving r-convex functions. J. Optimization Theory Appl. ~ (1973), , WILLIAMS (A.C.): Complementary geometric programming. SIAM J. Appl. Math..!2. (1970), , --: On the primal and dual constraint sets in geometric programming. J. Math. Anal. Appl. E (1970), & , ZANG (I.): Generalized convex functions with applications to nonlinear programming. [Van Moeseke, 1974], pp AZPEITIA (A.G.): General izations and remarks on the Farkas-Minkowski and Kuhn Tucker theorems (Spanish). Rev. Colombiana Mat. ~ (1970), : Extensions of the Farkas-Minkowski and the Kuhn-Tucker theorems. Elektron. Informationsverarbeit. Kybernetik I (1971), BABICH (M.D.), IVANOV (V.V.): Investigation of the total error in problems of minimizing functionals under constraints (Russian). Ukrain. Mat. Z. ~ (1969), BACHMANN (G.), ELSTER (K.-H.), PETRY (K.): Zur Problemstellung der geometrischen Opt imierung. Wiss. Z. Techn. Hochsch. Ilmenau.!2. (1973), no. 1, BALAS (E.): Minimax and dual ity for I inear and nonl inear mixed-integer programming. [Abadie, 1970], pp : A dual ity theorem and an algorithm for (mixed-) integer nonl inear programming. Linear Algebra and Appl. ~ (1971), BALINSKI (M.L.), BAUMOL (W.J.): The dual in nonl inear programming and its economic interpretation. Rev. Economic Studies 12 (1968), BANDLER (J.W.), CHARALAMBOUS (C.): Nonlinear programming using minimax techniques. J. Optimization Theory Appl. II (1974), BANKOFF (S.G.): Connection theorems in non-convex programming. Internat. J. Control I (1968), BARANKIN (E.W.), DORFMAN (R.): On quadratic programming. University of Cal ifornia Publ ications in Statistics, Vol. 2, pp University of Cal ifornia Press, Berke I ey, 1958.

10 Bibliographie 341 BARD (V.), GREENSTADT (J.L.): A modified Newton method for optimization with equal ity constraints. [Fletcher, 19691, pp BARON (D.P.): Quadratic programming with quadratic constraints. Naval Res. logist. Quart. 11 (1972), BARR (R.O.): Computation of optimal controls on convex reachable sets. [Balakrishnan, Neustadt, 19671, pp : An efficient computational procedure for a general ized quadratic programming problem. SIAM J. Control I (1969), , GilBERT (E.G.): Some efficient algorithms for a class of abstract optimization problems arising in optimal control. IEEE Trans. Automatic Control AC-14 (1969), BARTELS (R.H.), GOLUB (G.H.), SAUNDERS (M.A.): Numerical techniques in mathematical programming. [Rosen, Mangasarian, Ritter, 1970], pp BASILE (G.), MARRO (G.): An analog method for computing the constrained minimum of a convex quadratic function. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 44 (1968), no. 1, BAUMOl (W.J.), BUSHNELL (R.C.): Error produced by 1 inearization in mathematical programming. Econometrica ~ (1967), BAZARAA (M.S.): A theorem of the alternative with appl ication to convex programming: optimality, duality, and stability. J. Math. Anal. Appl. ~ (1973), : Geometry and resolution of dual ity gaps. Naval Res. Logist. Quart. 20 (1973), , GOODE (J.J.): Necessary optimal ity criteria in mathematical programming in the presence of differentiabil ity. J. Math. Anal. Appl. 40 (1972), , ----: On symmetric dual ity in nonl inear programming. Operations Res. 21 (1973), , ----: Necessary optimal ity criteria in mathematical programming in normed I inear spaces. J. Optimization Theory Appl. 2l (1973), , ----: Extension of optimal ity conditions via supporting functions. Math. Programming ~ (1973), , ----, NASHED (M.Z.): A nonl inear complementarity problem in mathematical programming in Banach space. Proc. Amer. Math. Soc. ~ (1972), , --, ----: On the cones of tangents with applications to mathematical programming. J. Optimization Theory Appl. 11 (1974), , ----, SHETTY (C.M.): Optimality criteria in nonlinear programming without differentiabil ity. Operations Res. 11 (1971), , ----, ----: A unified nonl inear dual ity formulation. Operations Res. 19 (1971), , ----, ----: Constraint qual ifications revisited. Management Sci..!...!!. (1972), BEALE (E.M.L.): On minimizing a convex function subject to I inear inequalities. J. Roy. Statist. Soc. Ser. B..!l (1955), On quadratic programming. Naval Res. Logist. Quart. ~ (1959), Numerical methods. [Abadie, 19671, pp "---: Nonlinear optimization by simplex-like methods. [Fletcher, 19691, pp Computational methods for least squares. [Abadie, 19701, pp BECKERT (H.): Uber die Konvergenz des Gradientenverfahrens mit Anwendungen auf Standortprobleme und das Ritzsche Verfahren. Z. angew. Math. Mech. 51 (1971),

11 342 Bibliographie BECKMANN (M.J.), KAPUR (K.C.): Conjugate dual ity: some applications to economic theory. J. Economic Theory i (1972), BECTOR (C.R.): Nonl inear ind~finite functional programming with nonl inear constraints. Cahiers Centre Etudes Recherche Oper. 1 (1967), Nonl inear fractional functional programming with non I inear constraints. l. angew. Math. Mech. 48 (196H), : Dual ity in fractional and indefinite programming. l. angew. Math. Mech. 48 (1968), : Programming problems with convex fractional functions. Operations Res. 16 (1968), 3H : Some aspects of quasi-convex programming. l. angew. Math. Mech. 50 (1970), : Duality in nonlinear fractional programming. l. Operations Res...!l (1973), : On convexity).. pseudo-convexity and quasi-convexity of composite functions. Cahiers Centre Etudes Recherche Oper. li (1973), , GROVER (T.R.): On a sufficient Ol:ltimal ity theorem of Mangasarian in non I inear programming. Cahiers Centre Etudes Recherche Oper. ~ (1974), 3-6. BEJAR ALAMO (J.): Mathematical theory of programming (Spanish). Mem. Real Acad. Ci. Exact. Frs. Natur. Madrid ~, no. 2 (196]). --: Non-I inear programming. Comparison of several methods (Spanish). Trabajos Estad1'st. Investigacion Operacional 20 (1969), no. 1, BELENKIJ (V.l.): Mathematical programming problems with minimum point (Russian). Dokl. Akad. Nauk SSSR 183 (1968), Soviet Math. Dokl. 9 (196H), (Engl ish trans1.) BELLMAN (R.E.): Dynamic programming and Lagrange multipl iers. Proc. Nat. Acad. Sci. USA 42 (1956), , KARUSH (W.): Mathemat i ca 1 programmi ng and the maximum transform. SIAM J. Appl. Math.!Q (1962), BELLMORE (M.), GREENBERG (H.J.), JARVIS (J.J.): Generalized penalty function concepts in mathematical optimization. Operations Res. ~ (1970), BELTRAMI (E.J.): A computational approach to necessary conditions in mathematical programming. ICC Bull. ~ (1967), : On infinite-dimensional convex programs. J. Comput. System Sci. ~ (1967), : A constructive proof of the Kuhn-Tucker multiplier rule. J. Math. Anal. Appl. 26 (1969), : A comparison of some recent iterative methods for the numerical solution of nonlinear programs. Computing Methods in Optimization Problems (Lecture Notes in Operations Research and Mathematical Economics, 14), pp Springer, Berl in, BENDERS (J.F.): Partitioning in mathematical programming. Proefschrift, Rijksuniversiteit Utrecht, : Partitioning procedures for solving mixed-variables programming problems. Numer. Hath. ~ (1962), : Some aspects of mathematical optimization (Dutch). Euclides (Groningen) 43 (1968), BEN-ISRAEL (A.): On Newton's method in nonl inear programming. [Kuhn, 1970], pp , CHARNES (A.), KORTANEK (K. O. J: Dual i ty and asymptot i c sol vab iii ty over cones. Bull. Amer. Math. Soc. 75 (1969), ; erratum, ibid. 76 (1970), 426.

12 Bibliographie , --, --: Asymptotic dual ity over closed convex sets. J. Math. Anal. Appl. ~ (1971), , --, --: Asymptotic dual ity in semi-infinite programming and the convex core topology. Rendiconti Mat. i (1971), BENSOUSSAN (A.), KENNETH (P.): Sur 1 'analogie entre les methodes de regularisation et de penal isation. Rev. FranSaise Informat. Recherche Operationnel Ie ~ (1968), no. 13, BEREANU (B.): A property of convex, piecewise 1 inear functions with appl ications to mathematical programming. Unternehmensforschung 1 (1965), : On the composition of convex functions. Rev. Roumaine Math. Pures Appl. 2i (1969), : Quasi-convexity, strictly quasi-convexity and pseudo-convexity of composite objective functions. Rev. Fran~aise Automat. Informat. Recherche Operationnelle.. (1972), no. R-l, BERESNEV (V. V.): Necessary conditions for an extremum in convex maximin problems over connected sets (Russian). Kibernetika (Kiev) 1972, no. 1, : Necessary extremal conditions for maximin problems (Russian). Kibernetika (Kiev) 1973, no. 2, BERGER (A.), ELSTER (K.-H.), HEINE (G.): Zur Klassifizierung von L6sungsverfahren in der mathematischen Optimierung. Wiss. Z. Techn. Hochsch. Ilmenau 18 (1972), no. 3, BERGTHALLER (C.): Programmation quadratique quasi convexe. C.R. Acad. Sci. Paris Ser. A ~ (1971), BERKOVITZ (L.D.): Variational methods in problems of control and programming. J. Math. Anal. Appl. 1. (1961), BERNADAT (J.): Programmes quadratiques. [Fortet et al., 1964], pp BERNHOLTZ (B.): A new derivation of the Kuhn-Tucker conditions. Operations Res. ~ (1964), BERSHCHANSKIJ (Ja.My): A method for solving 1 inear and convex programming problems (Russian). Z. Vy~isl. Mat. i Mat. Fiz. 10 (1970), USSR Comput. Math. and Math. Phys...!.Q (1970), no. 3, 85-95(English transl.). BERTSEKAS (D.P.), MITTER (S.K.): A descent numerical method for optimization problems with nondifferentiable cost functionals. SIAM J. Control 11 (1973), BHATIA (D.): A note on dual ity theorem for a nonl inear programming problem. Management Sci. ~ (1970), , KAUL (R.N.): Nonl inear programming in complex space. J. Math. Anal. Appl. ~ (1969), BHATT (S.K.): Sequential unconstrained minimization technique for a non-convex program. Cahiers Centre Etudes Recherche Oper. ~ (1973), : General ized p-seudo-convex programming in real Banach space and dual ity. Cahiers Centre Etudes Recherche Oper. ~ (1974), BIGELOW (J.H.), SHAPIRO (N.Z.): Optimization problems with large parameters. SIAM J. Appl. Math. ~ (1973), , --: Impl icit function theorems for mathematical programming and for systems of inequal ities. Math. Programming.. (1974), BIGG (M.D.): The minimization of a general function subject to a set of non-i inear constraints. Proc. Cambridge Philos. Soc. 59 (1963), BIGGS (M.C.): Constrained minimization using recursive equal ity quadratic programming. [Lootsma, 1972], pp

13 344 Bibliographie BIRZAK (B.), PSHENICHNYJ (B.N.): Minimization problems for non-smooth functions (Russian). Kibernetika (Kiev) 1966, no. 6, BITTNER (L.): Eine Verallgemeinerung des Verfahrens des logarithmischen Potentials von Frisch fur nichtl ineare Optimierungsprobleme. [Prekopa, 1965], pp : BegrUndung des sogenannten diskreten Maximumprinzips. Z. Wahrscheinl ichkeitstheorie verw. Gebiete 1 (1968), : Abschatzungen bei Variationsmethoden mit Hilfe von Dualitatssatzen. I, II. Numer. Math. 21 (1968), ; ~ (1971), 2B : Some representation theorems for functions and sets, and their application. to nonlinear programming. Numer. Math. ~ (1970), : New conditions for the val idity of the Lagrange multipl ier rule. I. Math. Nachr. 48 (1971), : Quasilinearization and primal-dual-relations of Chebyshev-approximation. I. Math. Operationsforschung Statist. 1 (1972), : On I i near i nequa lit i es (moment i nequa lit i es) and some resu I ts of Ky Fan. Math. Nachr. 64 (1974), BLUM (E.), OETTLI (W.): Direct proof of the existence theorem for quadratic programming. Operations Res. 20 (1972), BOD (P.): Uber "indifferente" Optimierungsaufgaben. Operations Research Verfahren ~ (1973), BOLTJANSKIJ (V.G.): Necessary conditions in problems of mathematical programming and discrete optimization (Russian). Mat. Issled. I (1972), no. 4, : Necessary conditions for the extremum of a function (Russian). Differencialnye Uravnenija ~ (1972), 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 l! (1963), : On sensitivity analysis in convex quadratic programming problems. Operations Res. ~ (1963), BOUZITAT (J.): Les conditions de Kuhn et Tucker en programmation mathematique. Cahiers Bur. Univ. Recherche Oper. (Paris) 1969, no. 12, 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. 2 (1966), BRACKEN (J.), FALK (J.E.), McGILL (J.T.): The equivalence of two mathematical programs with optimization problems in the constraints. Operations Res. 22 (1974), , McGILL (J.T.): Mathematical programs with optimization problems in the constraints. Operations Res. ~ (1973), , --: A method for solving mathematical programs with nonl inear programs in the constraints. Operations Res. 22 (1974), BRAGARD (L.): Programmation quasi-concave. Bull. Soc. Roy. Sci. Liege 39 (1970), 478-4!l5.

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