Anhang. Bibliographie zur Nichtlinearen Programmierung

Anhang Bibliographie zur Nichtlinearen Programmierung

Bibliographie 333 A. Lehrbucher und Monographien ADBY (P.R.), DEMPSTER (M.A. H.) : Introduction to Optimization Methods. Chapman and Hall, London, 1974. AOKI (M.): Introduction to Optimization Techniques. Macmillan, New York, 1971 ARROW (K.J.), HAHN (F.H.): General Competitive Analysis. Holden-Day, San Francisco, 1971. 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, 1972. BALAKRISHNAN (A.V.): Introduction to Optimization Theory in a Hilbert Space (Lecture Notes in Operations Research and Mathematical Systems, 42). Springer, Ber! in, 1971. BELTRAMI (LJ.): An Algorithmic Approach to Nonl inear Analysis and Optimization. Academic Press, New York, 1970. BERGE (C.): Espaces topologiques, fonctions multivoques (deuxieme edition). Dunod, Paris, 1966. BERGE (C.), GHOUl LA-HOURI Dunod, Paris, 1962. (A.): Programmes, jeux et reseaux de transport. BERMAN (A.): Cones, Matrices and Mathematical Programming (Lecture Notes in Economics and Mathematical Systems, 79). Springer, Berlin, 1973. BOOT (J.C.G.): Quadratic Programming. North-Holland, Amsterdam, 1964. BOX (M.J.), DAVIES (D.), SWANN (W.H.): Non-Linear Optimization Techniques. 01 iver and Boyd,. Edinburgh, 1969. BRACKEN (J.), McCORMICK (G.P.): Selected Appl ications of Nonl inear Programming. Wiley, New York, 1968. BRENT (R.P.): Algorithms for Minimization without Derivatives. Prentice Hall, Englewood Cliffs, 1973. CANON (M.D.), CULLUM (C.D.), POLAK (E.): Theory of Optimal Control and Mathematical Programming. McGraw-Hill, New York, 1970. CEA (J.): Optimisation: theorie et algorithmes. Dunod, Paris, 1971. COLLATZ (L.), WETTERLING (W.): Optimierungsaufgaben (2. Auflage). Springer, Ber! in, 1971. DANIEL (J.W.): The Approximate Minimization of Functionals. Prentice-Hall, Englewood Cl i ffs, N.J., 1971. DANSKIN (J.M.): The Theory of Max-Min. Springer, Berlin, 1967. DANTZIG (G.B.): Linear Programming and Extensions. Princeton University Press, Princeton, 1963. 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, 1970. DENNIS (J.B.): Mathematical Programming and Electrical Networks. Wiley, New York, 1959.

334 Bibliographie DIXON (L.C.W.): Nonl inear Optimisation. The Engl ish Universities Press, London, 1972. DUFFIN (R.J.), PETERSON (E.L.), ZENER (C.): Geometric Programming. Wiley, New York, 1967. EGGLESTON (H.G.): Convexity. Cambridge University Press, Cambridge, 1963. EKELAND (I.), TEMAM (R.): Analyse convexe et problemes variationnels. Dunod, Paris, 1974. 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, 1971. FIACCO (A.V.), McCORMICK (G.P.): Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York, 1968. FR~NKEL (H.): Diskrete optimale Steuerungsprobleme und konvexe Optimierung. Walter de Gruyter, Berl in, 1971. GIRSANOV (I.V.): Lectures on Mathematical Theory of Extremum Problems (Lecture Notes in Economics and Mathematical Systems, 67). Springer, Be r lin, 1972. GOLDSTEIN (A.A.): Constructive Real Analysis. Harper & Row, New York, 1967. GOLSTEIN (E.G.): Theory of Convex Programming (Translations of Mathematical Monographs, Vol.36). American Mathematical Society, Providence, R.I., 1972. GoPFERT (A.): Mathematische Optimierung in allgemeinen Vektorraumen. B.G. Teubner, Leipzig, 1973. HADLEY (G.): Nonl inear and Dynamic Programming. Addison-Wesley, Reading, Mass., 1964. HESTENES (M.R.): Calculus of Variations and Optimal Control Theory. Wiley, New York, 1966. HIMMELBLAU (D.M.): Appl ied Nonl inear Programming. McGraw-Hili, New York, 1972. HOLMES (R.B.): A Course on Optimization and Best Approximation (Lecture Notes in Mathematics, 257). Springer, Berl in, 1972. INTRILIGATOR (M.D.): Mathematical Optimization and Economic Theory. Prentice-Hal I, Englewood CI iffs, N.J., 1971. JACOBY (S.L.S.), KOWALIK (J.S.), PIZZO (J.T.): Iterative Methods for Nonlinear Optimization Problems. Prentice-Hal I, Englewood CI iffs, N.J., 1972. KARLIN (S.): Mathematical Methods and Theory in Games, Programming, and Economics, 2 Vols. Addison-Wesley, Reading, Mass., 1959. KOWALIK (J.), OSBORNE (M.R.): Methods for Unconstrained Optimization Problems. American Elsevier, New York, 1968. KUNZI (H.P.), KRELLE (W.): Nichtl ineare Programmierung. Springer, Berl in, 1962. 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, 1969. KUNZI (H.P.), TZSCHACH (H.G.), ZEHNDER (C.A.): Numerische Methoden der mathematischen Optimierung. B.G. Teubner, Stuttgart, 1967.

Bibliographie 335 LASDON (L.S.): Optimization Theory for Large Systems. Macmil lan, New York, 1970. LAURENT (P.-J.): Approximation et optimisation. Hermann, Paris, 1972. LUENBERGER (D.G.): Optimization by Vector Space Methods. Wiley, New York, 1969. LUENBERGER (D.G.): Introduction to Linear and Nonl inear Programming. Addison-Wesley, Reading, Mass., 1973. MANGASARIAN (O.L.): Nonl inear Programming. McGraw-Hill, New York, 1969. NEUSTADT (L.W.): Optimization. Princeton University Press, Princeton, 1974. NIKAIDO (H.): Convex Structures and Economic Theory. Academic Press, New York, 1968. POLAK (E.): Computational Methods in Optimization. Academic Press, New York, 1971. PSHENICHNYI (B.N.): Necessary Conditions for an Extremum. Marcel Dekker, New York, 1971. ROBERTS (A.W.), VARBERG (D.E.): Convex Functions. Academic Press, New York, 1973. ROCKAFELLAR (R.T.): Convex Analysis. Princeton University Press, Princeton, 1970. ROCKAFELLAR (R.T.): Conjugate Dual ity and Optimization. Society for Industrial and Appl ied Mathematics, Philadelphia, 1974. RUSSEL (D.L.): Optimization Theory. W.A. Benjamin, New York, 1970. SANDER (H.-J.): Dual itat bei Optimierungsaufgaben. R. Oldenbourg, MUnchen, 1973. SCARF (H.), HANSEN (T.): The Computation of Economic Equil ibria. Yale University Press, New Haven, 1973. STOER (J.), WITZGALL (C.): Convexity and Optimization in Finite Dimensions. I. Springer, Berl in, 1970. SUCHOWITZKI (S.I.), AWDEJEWA (L.I.): Lineare und konvexe Programmierung. R. Oldenbourg, MUnchen, 1969. TABAK (D.), KUO (B.C.): Optimal Control by Mathematical Programming. Prentice-Hall, Englewood Cl iffs, 1971. VAJDA (S.): Mathematical Programming. Addison-Wesley, Reading, Mass., 1961. VAJDA (S.): Theory of Linear and Non-Linear Programming. Longman, London, 1974. VALENTINE (F.A.): Convex Sets. McGraw-Hi 1 1, New York, 1964. VAN DE PANNE (C.): Methods for Linear and Quadratic Programming. North Holland, Amsterdam, 1974. VARAIYA (P.P.): Notes on Optimization. Van Nostrand Reinhold, New York, 1972. WHITTLE (P.): Optimization under Constraints. Wiley-Interscience, London, 1971. WILDE (D.J.): Optimum Seeking Methods. Prentice-Hal I, Englewood Cl iffs, N. J., 1964. WILDE (D.J.), BEIGHTLER (C.S.): Foundations of Optimization. Prentice Ha 11, Eng 1 ewood eli f f s, N. J., 1964.

336 Bibliographie ZANGWILL (W. I.): Nonl inear Programming. Prentice-Hall, Englewood Cl iffs, N. J., 1969. ZOUTENDIJK (G.): Methods of Feasible Directions. Elsevier, Amsterdam, 1960. B. Sammelbande ABADIE (J.), ed.: Nonl inear Programming. North-Holland, Amsterdam, 1967. ABADIE (J.), ed.: Integer and Nonl inear Programming. North-Holland, Amsterdam, 1970. ANDERSSEN (R.S.), JENNINGS (L.S.), RYAN (D.M.), eds.: Optimization. University of Queensland Press, St. Lucia, Queensland, 1972. ARROW (K.J.), HURWICZ (L.), UZAWA (H.), eds.: Studies in Linear and Non- 1 inear Programming. Stanford University Press, Stanford, 1958. AVRIEL (M.), RIJCKAERT (M.J.), WILDE (D.J.), eds.: Optimization and Design. Prentice-Hall, Englewood Cl iffs, N.J., 1973. BALAKRISHNAN (A.V.), ed.: Techniques of Optimization. Academic Press, New York, 1972. BALAKRISHNAN (A.V.), NEUSTADT (L.W.), eds.: Mathematical Theory of Control. Academic Press, New York, 1967. BEALE (E.M.L.), ed.: Appl ications of Mathematical Programming Techniques. Engl ish Universities Press, London, 1970. BELLMAN (R.), ed.: Mathematical Optimization Techniques. University of Cal i fornia Press, Berkeley, 1963. BROISE (P.), HUARD (P.), SENTENAC (J.): Decomposition des programmes mathematiques (Monographies de recherche operationnelle, 6). Dunod, Paris, 1968. COLLATZ (L.), WETTERLING (W.), Hrsg.: Numerische Methoden bei Optimierungsaufgaben (ISNM, Vo1.1n. Birkhauser, Basel, 1973. CONTI (R.), RUBERTI (A.), eds.: 5th Conference on Optimization Techniques, Part I (Lecture Notes in Computer Science, 3): Springer, Berl in, 1973. 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., 1968. FLETCHER (R.), ed.: Optimization. Academic Press, London, 1969. FORTET (R.), et al.: Mathematique des programmes economiques (Monographies de recherche operationnel Ie, I). Dunod, Paris, 1964. GEOFFRION (A.M.), ed.: Perspectives on Optimization. Addison-Wesley, Reading, Mass., 1972. GHIZZETTI (A.), ed.: Theory and Appl ications of Monotone Operators (Proceedings of a NATO Advanced Study Institute, Venice). Edizioni Oderisi, Gubbio, 1969. GRAVES (R.L.), WOLFE (P.), eds.: Recent Advances in Mathematical Programming. McGraw-Hi 1 1, New York, 1963. HIMMELBLAU (D.M.), ed.: Decomposition of Large-Scale Problems. North-Holland, Amsterdam, 1973. KOOPMANS (T.C.), ed.: Activity Analysis of Production and Allocation. Wiley, New York, 1951. KUHN (H.W.), ed.: Proceedings of the Princeton Symposium on Mathematical Programming. Princeton University Press, Princeton, 1970.

Bibliographie 337 KUHN (H.W.), SZEGo (G.P.), eds.: Differential Games and Related Topics. North Hoi land, Amsterdam, 1971. KUHN (H.W.), TUCKER (A.W.), eds.: Linear Inequal ities and Related Systems (Annals of Mathematics Studies, no.3~). Princeton University Press, Princeton, 1956. LAVI (A.), VOGL (T.P.), eds.: Recent Advances in Optimization Techniques. Wiley, New York, 1966. LOOTSMA (F.A.), ed.: Numerical 11ethods for Non-l inear Optimization. Academic Press, New York, 1972. ~O! (J.), ~O~ (M.W.), eds.: Mathematical Models in Economics. North-Holland, Amsterdam, 1974. VAN MOESEKE (P.), ed.: Mathematical Programs for Activity Analysis. North Holland, Amsterdam, 1974. MURRAY (W.), ed.: Numerical Methods for Unconstrained Optimization. Academic Press, London, 1972. PREKOPA (A.), ed.: Colloquium on Appl ications of Mathematics to Economics. Akademiai Kiadb, Budapest, 1965. ROSEN (J.B.), MANGASARIAN (O.L.), RITTER (K.), eds.: Nonl inear Programming. Academic Press, New York, 1970. SZEGo (G.P.), ed.: Minimization Algorithms. Mathematical Theories and Computer Results. Academic Press, New York, 1972. ZADEH (L.A.), NEUSTADT (L.W.), BALAKRISHNAN (A.V.), eds.: Computing Methods in Optimization Problems - 2. Academic Press, New York, 1969. c. Aufsatze *) ABADIE (J.): Programmation mathematique. Actes du 5eme Congres AFIRO, pp. 44-67. Association Fransaise d' Informatique et de Recherche Operationnel Ie, Paris, 1966. --: On the Kuhn-Tucker theorem. [Abadie, 1967l, pp. 19-36. --: Appl ication of the GRG algorithm to optimal control problems. [Abadie, 1970l, pp. 191-211. --: Simplex-l ike methods for non-l inear programming. [Szego, 1972l, pp. 41-60. --, CARPENTIER (J.): Generalization of the Wolfe reduced gradient method to the case of nonl inear constraints. [Fletcher, 1969], pp. 37-47. ABLOW (C.M.), BRIGHAM (G.): An analog solution of programming problems. Operations Res. 1 (1955), 388-394. ABRAMS (R.A.): Nonl inear Programming in complex space: Sufficient conditions and dual ity. J. Math. Anal. Appl. ~ (1972), 619-632., BEN-ISRAEL (A.): A dual ity theorem for complex quadratic programming. J. Optimization Theory Appl. ~ (1969), 244-252. --, --: Nonl inear programming in complex space: Necessary conditions. SIAM J. Control 1 (1971),606-620. ABRHAM (J.): An approximate method for convex programming. Econometrica ~ (1961), 700-703. *) 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".

338 Bibliographie --: The multiplex method and its appl ication to concave programming. Czechoslovak Math. J. ~ (1962), 325-345. --, ARRI (P.S.): Approximation of separable functions in convex programming. INFOR - Canad. J. Operational Res. and Information Processing ~ (1973), 245-252. ADACHI (N.): On variable-metric algorithms. J. Optimization Theory Appl. I (1971), 391-410. AFRIAT (S.N.): The progressive support method for convex programming. SIAM J. Numer. Anal. I (1970), 447-457. --: Theory of maxima and the method of Lagrange. SIAM J. Appl. Math. 20 (1971), 343-357. --: The output I imit function in general and convex programming and the theory of production. Econometrica 12 (1971), 309-339. AGGARWAL (S.P.): A note on quasiconvex programming. Metrika ~ (1968), 97-105. AGMON (S.): The relaxation method for linear inequal ities. Canad. J. Math. 6 (1954), 382-392. - 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), 171-177. ALTMAN (M.): Stationary points in non-i inear programming. Bull. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. ~ (1964), 29-35. --: A feasible direction method for solving the nonl inear programming problem. Bull. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. ~ (1964), 43-50. --: A general ized gradient method for the conditional minimum of a functional. Bull. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. ~ (1966), 445-451. --: 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, 19-24. --: A general ized gradient method for the conditional extremum of a function. Bull. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. ~ (1967), 177-183. --: Bilinear Programming. Bull. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. ~ (1968), 741-746. --: A general maximum principle for optimization problems. Studia Math. ~ (1968), 319-329. --: 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),13-27. ----: Theoreme general de separation des appl ications. Dual ite dans la programmation mathematique. Fonctions duales. C.R. Acad. Sci. Paris Ser. A 269 (1969), 198-201. - --: A general separation theorem for mappings, saddle-points, dual ity, and conjugate functions. Studia Math. 36 (1970), 131-166. --: A general maximum principle for optimization problems with operator inequalities. Boll. Unione Mat. Ital.!: (1970),283-292. 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, 26-33. ARIMOTO (S.): On a multistage nonl inear programming problem. J. Math. Anal. Appl. Jl (196 7J, 161-171. ARMACOST (R.L.), FIACCO (A.V.): Computational experience in sensitivity analysis for nonl inear programming. Math. Programming ~ (1974), 301-326.

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), 779-800. -----, GOULD (F.J.), HOWE (S.M.): A general saddle point result for constrained optimization. Math. Programming 2 (1973), 225-234. -----, HURWICZ (L.): Reduction of constrained maxima to saddle-point problems. Proceedings of the 3rd Berkeley Symposium on Mathematical Statistics and Probability, Vol. 5, pp. 1-20. University of California Press, Berkeley, 1956., Gradient methods for constrained maxima. Operations Res. 2 (1957), 258-265. -----, ----- Gradient method for concave programming. I, III. [Arrow, Hurwicz, Uzawa, 1958], pp. 117-126; pp. 133-145. -----, -----, UZAWA (H.): Constraint qualifications in maximization problems. Naval Res. Logist. Quart.! (1961), 175-191. -----, SOLOW (R.M.): Gradient methods for constrained maxima, with weakened assumptions. [Arrow, Hurwicz, Uzawa, 1958], pp. 166-176. 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), 665-674. ASAADI (J.): A computational comparison of some non-l inear programs. Math. Programming ~ (1973), 144-154. ASTAFEV (N.N.): On the direct and the inverse dual ity theorem in convex programming (Russian). Optimal. Planirovanie ~ (1969),137-149. -----: On general ized inverse dual ity theorems in convex programming problems (Russian). Dokl. Akad. Nauk SSSR 199 (1971), 511-514. Soviet ~lath. Dokl. 12 (1971), 1082-1086 (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), 132-139. AUBIN (J.-P.): Characterization of the sets of constraints for which the necessary conditions for optimization problems hold. SIAM J. Control! (1970), 14ti-162. -----: A Pareto minimum principle. [Kuhn, Szego, 1971l, pp. 147-175. -----: Theoreme du minimax pour une classe de fonctions. C.R. Acad. Sci. Paris Ser. A 274 (1972), 455-458. -----: Multipl icateurs de Kuhn-Tucker pour des jeux non cooperatifs contraints. Ann. Scuola Norm. Sup. Pisa '!:l. (1973),561-589. -----, 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), 547-549. AUSLENDER (A.): Methodes du second ordre dans les problemes d'optimisation avec contraintes. Rev. Franjaise Informat. Recherche Operationnelle 1 (1969), no. R-2, 27-42. -----: Recherche des points de selle d'une fonction. Symposium on Optimization (Lecture Notes in Mathematics, 132), pp. 37-52. Springer, Berl in, 1970. -----: Recherche des points de selle d'une fonction. Cahiers Centre Etudes Recherche Oper. ~ (1970), 57-75. -----: Methodes et theoremes de dua lite. Rev. Frania i se I nformat. Recherche Operationnelle ~ (1970), no. 1, 9-45.

340 Bibliographie --: Methodes numer'ques pour la decomposition et la minimisation de fonctions non differentiables. Numer. Math. ~ (1971), 213-223. : Une methodes generale pour la resolution et la decomposition de problemes de cols avec contraintes. C.R. Acad. Sci. Paris Ser. A 272 (1971), 1582-1585. --: 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, 53-56. --: Resolution numerique d'inegalites variationnelles. Rev. Franiaise Automat. Informat. Recherche Operationnel Ie I (1973), no. R-2, 67-72. --, 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. 1-40. Springer, Berl in, 1974. --, MARTINET (B.): Methodes de decomposition pour la minimisation d'une fonctionnelle sur un espace produit. C.R. Acad. Sci. Paris Ser. A 274 (1972), 632-635. AVDEEVA (L. I.): Appl ication of convex programming methods to the solution of Chebyshev approximation problems (Russian). Kibernetika (Kiev) 1969, no. 3, 89-93. AVRIEL (M.): Fundamentals of geometric programming. [Beale, 1970], pp. 295-312. r-convex functions. Math. Programming ~ (1972), 309-323. Solution of certain nonl inear programs involving r-convex functions. J. Optimization Theory Appl. ~ (1973), 159-174., WILLIAMS (A.C.): Complementary geometric programming. SIAM J. Appl. Math..!2. (1970), 125-141., --: On the primal and dual constraint sets in geometric programming. J. Math. Anal. Appl. E (1970), &84-688. --, ZANG (I.): Generalized convex functions with applications to nonlinear programming. [Van Moeseke, 1974], pp. 23-33. AZPEITIA (A.G.): General izations and remarks on the Farkas-Minkowski and Kuhn Tucker theorems (Spanish). Rev. Colombiana Mat. ~ (1970), 41-50. ----: Extensions of the Farkas-Minkowski and the Kuhn-Tucker theorems. Elektron. Informationsverarbeit. Kybernetik I (1971), 31-34. BABICH (M.D.), IVANOV (V.V.): Investigation of the total error in problems of minimizing functionals under constraints (Russian). Ukrain. Mat. Z. ~ (1969), 3-14. BACHMANN (G.), ELSTER (K.-H.), PETRY (K.): Zur Problemstellung der geometrischen Opt imierung. Wiss. Z. Techn. Hochsch. Ilmenau.!2. (1973), no. 1, 3-39. BALAS (E.): Minimax and dual ity for I inear and nonl inear mixed-integer programming. [Abadie, 1970], pp. 385-418. --: A dual ity theorem and an algorithm for (mixed-) integer nonl inear programming. Linear Algebra and Appl. ~ (1971), 341-352. BALINSKI (M.L.), BAUMOL (W.J.): The dual in nonl inear programming and its economic interpretation. Rev. Economic Studies 12 (1968), 237-256. BANDLER (J.W.), CHARALAMBOUS (C.): Nonlinear programming using minimax techniques. J. Optimization Theory Appl. II (1974), 607-619. BANKOFF (S.G.): Connection theorems in non-convex programming. Internat. J. Control I (1968),447-449. BARANKIN (E.W.), DORFMAN (R.): On quadratic programming. University of Cal ifornia Publ ications in Statistics, Vol. 2, pp. 285-317. University of Cal ifornia Press, Berke I ey, 1958.

Bibliographie 341 BARD (V.), GREENSTADT (J.L.): A modified Newton method for optimization with equal ity constraints. [Fletcher, 19691, pp. 299-306. BARON (D.P.): Quadratic programming with quadratic constraints. Naval Res. logist. Quart. 11 (1972), 253-260. BARR (R.O.): Computation of optimal controls on convex reachable sets. [Balakrishnan, Neustadt, 19671, pp. 63-70. -----: An efficient computational procedure for a general ized quadratic programming problem. SIAM J. Control I (1969), 415-429. ----, GilBERT (E.G.): Some efficient algorithms for a class of abstract optimization problems arising in optimal control. IEEE Trans. Automatic Control AC-14 (1969), 640-652. BARTELS (R.H.), GOLUB (G.H.), SAUNDERS (M.A.): Numerical techniques in mathematical programming. [Rosen, Mangasarian, Ritter, 1970], pp. 123-176. 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, 45-53. BAUMOl (W.J.), BUSHNELL (R.C.): Error produced by 1 inearization in mathematical programming. Econometrica ~ (1967), 447-471. BAZARAA (M.S.): A theorem of the alternative with appl ication to convex programming: optimality, duality, and stability. J. Math. Anal. Appl. ~ (1973), 701-715. ----: Geometry and resolution of dual ity gaps. Naval Res. Logist. Quart. 20 (1973), 357-365. ----, GOODE (J.J.): Necessary optimal ity criteria in mathematical programming in the presence of differentiabil ity. J. Math. Anal. Appl. 40 (1972), 609-621. -----, ----: On symmetric dual ity in nonl inear programming. Operations Res. 21 (1973), 1-9. ----, ----: Necessary optimal ity criteria in mathematical programming in normed I inear spaces. J. Optimization Theory Appl. 2l (1973), 235-244. ----, ----: Extension of optimal ity conditions via supporting functions. Math. Programming ~ (1973), 267-285. ----, ----, NASHED (M.Z.): A nonl inear complementarity problem in mathematical programming in Banach space. Proc. Amer. Math. Soc. ~ (1972), 165-170. ----, --, ----: On the cones of tangents with applications to mathematical programming. J. Optimization Theory Appl. 11 (1974), 389-426. ----, ----, SHETTY (C.M.): Optimality criteria in nonlinear programming without differentiabil ity. Operations Res. 11 (1971), 77-86. ----, ----, ----: A unified nonl inear dual ity formulation. Operations Res. 19 (1971),1097-1100. - ----, ----, ----: Constraint qual ifications revisited. Management Sci..!...!!. (1972), 567-573. BEALE (E.M.L.): On minimizing a convex function subject to I inear inequalities. J. Roy. Statist. Soc. Ser. B..!l (1955), 173-184. On quadratic programming. Naval Res. Logist. Quart. ~ (1959), 227-244. Numerical methods. [Abadie, 19671, pp. 133-205. -"---: Nonlinear optimization by simplex-like methods. [Fletcher, 19691, pp. 21-36. Computational methods for least squares. [Abadie, 19701, pp. 213-227. BECKERT (H.): Uber die Konvergenz des Gradientenverfahrens mit Anwendungen auf Standortprobleme und das Ritzsche Verfahren. Z. angew. Math. Mech. 51 (1971), 333-343. -

342 Bibliographie BECKMANN (M.J.), KAPUR (K.C.): Conjugate dual ity: some applications to economic theory. J. Economic Theory i (1972), 292-302. BECTOR (C.R.): Nonl inear ind~finite functional programming with nonl inear constraints. Cahiers Centre Etudes Recherche Oper. 1 (1967), 172-179. Nonl inear fractional functional programming with non I inear constraints. l. angew. Math. Mech. 48 (196H), 284-286. --: Dual ity in fractional and indefinite programming. l. angew. Math. Mech. 48 (1968),418-420. --: Programming problems with convex fractional functions. Operations Res. 16 (1968), 3H3-391. --: Some aspects of quasi-convex programming. l. angew. Math. Mech. 50 (1970), 495-497. --: Duality in nonlinear fractional programming. l. Operations Res...!l (1973), 183-193. --: On convexity).. pseudo-convexity and quasi-convexity of composite functions. Cahiers Centre Etudes Recherche Oper. li (1973), 411-428. --, 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, 17-34. BELENKIJ (V.l.): Mathematical programming problems with minimum point (Russian). Dokl. Akad. Nauk SSSR 183 (1968), 15-17. Soviet Math. Dokl. 9 (196H), 1301-1303 (Engl ish trans1.)-. - - BELLMAN (R.E.): Dynamic programming and Lagrange multipl iers. Proc. Nat. Acad. Sci. USA 42 (1956), 767-769. --, KARUSH (W.): Mathemat i ca 1 programmi ng and the maximum transform. SIAM J. Appl. Math.!Q (1962), 550-566. BELLMORE (M.), GREENBERG (H.J.), JARVIS (J.J.): Generalized penalty function concepts in mathematical optimization. Operations Res. ~ (1970), 229-252. BELTRAMI (E.J.): A computational approach to necessary conditions in mathematical programming. ICC Bull. ~ (1967), 265-273. ----: On infinite-dimensional convex programs. J. Comput. System Sci. ~ (1967), 323-329. --: A constructive proof of the Kuhn-Tucker multiplier rule. J. Math. Anal. Appl. 26 (1969), 297-306. --: 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. 20-29. Springer, Berl in, 1969. BENDERS (J.F.): Partitioning in mathematical programming. Proefschrift, Rijksuniversiteit Utrecht, 1960. --: Partitioning procedures for solving mixed-variables programming problems. Numer. Hath. ~ (1962), 238-252. --: Some aspects of mathematical optimization (Dutch). Euclides (Groningen) 43 (1968), 241-253. BEN-ISRAEL (A.): On Newton's method in nonl inear programming. [Kuhn, 1970], pp. 339-352. --, 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), 318-324; erratum, ibid. 76 (1970), 426.

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