Introduction to the volume

Jean-Paul Penot

Mémoires de la Société Mathématique de France (1979)

  • Volume: 60, page 7-24
  • ISSN: 0249-633X

How to cite

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Penot, Jean-Paul. "Introduction to the volume." Mémoires de la Société Mathématique de France 60 (1979): 7-24. <http://eudml.org/doc/94805>.

@article{Penot1979,
author = {Penot, Jean-Paul},
journal = {Mémoires de la Société Mathématique de France},
keywords = {non-convex analysis; historical overview; extensive bibliography of contemporary articles; generalizations of convexity},
language = {eng},
pages = {7-24},
publisher = {Société mathématique de France},
title = {Introduction to the volume},
url = {http://eudml.org/doc/94805},
volume = {60},
year = {1979},
}

TY - JOUR
AU - Penot, Jean-Paul
TI - Introduction to the volume
JO - Mémoires de la Société Mathématique de France
PY - 1979
PB - Société mathématique de France
VL - 60
SP - 7
EP - 24
LA - eng
KW - non-convex analysis; historical overview; extensive bibliography of contemporary articles; generalizations of convexity
UR - http://eudml.org/doc/94805
ER -

References

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  1. J.C. AGGERI : Isomorphisme d'un cône convexe abstrait à un cône fonctionnel. J. Math. Pures et Appl. 52 (4) (1973) 443-451. Zbl0279.20050MR50 #10756
  2. S. ALEXANDER - R.L. BISHOP (1974) : Convex supporting domains on spheres. Illinois J. Math. 18, 37-47. Zbl0272.53026MR48 #7158
  3. T.S. ANGEL (1976) : Existence of optimal control without convexity and a Bang-Bang theorem for linear Volterra equations. J. Optim. Th. and Appl. 19 (1), 63-79. Zbl0305.49022MR55 #3907
  4. P. ANTOINE (1976) : Conditions pour un minimum local d'une fonction différentiable. Pub. U.E.R. Math. Univ. Lille I N° 97. Zbl0427.49019
  5. P. ANTOINE - F. Van ISEGHEM (1976) : Conditions nécessaires et conditions suffisantes pour un minimum local d'une fonctionnelle. C.R. Acad. Sc. Paris 282, 523-526. Zbl0329.49009MR53 #9292
  6. A.A. ANTOZIEWICZ - A. CELLINA (1975) : Continuous selections and differential relations. J. Diff. Eq. 19, 386-398. Zbl0279.54007MR55 #3373
  7. K.J. ARROW - A. ENTHOVEN (1961) : Quasiconcave programming. Econometrica. 29, 779-800. Zbl0104.14302MR25 #1956
  8. E. ASPLUND (1966) : Farthest points in reflexive locally uniformly rotund Banach spaces. Israel J. Math. 4, 213-216. Zbl0143.34904MR34 #6480
  9. J-P. AUBIN (1974) : Analyse convexe et ses applications. Comptes-rendus, Lectures Notes in Economics and Mathematical Systems n° 102, Springer-Verlag. Zbl0285.00008MR50 #8190
  10. J-P. AUBIN (1979) : Mathematical methods of game and economic theory. North Holland, Amsterdam. Zbl0452.90093MR83a:90005
  11. J-P. AUBIN - F. CLARKE (1976) : Monotone trajectories of non-convex multivalued dynamical systems. MRC Tech. Report. Univ. of Wisconsin, Madison. 
  12. J-P. AUBIN - I. EKELAND (1976) : Estimates of the duality gap in nonconvex optimization, Math. of Operations Research 1, 225-245. Zbl0366.90102MR56 #7996
  13. R.J. AUMANN - M. PERLES (1965) : A variational problem arising in economics. J. Math. Anal. Appl. 11, 488-503. Zbl0137.39201MR31 #6670
  14. A. AUSLENDER (1976) : Convex analysis and its applications. Proceedings Conf. Murat le Quaire. Lecture Notes in Economics and Mathematical systems n°144. Zbl0342.00012MR56 #1161
  15. A. AUSLENDER (1977) : Minimisation sans contraintes de fonctions localement lipschitziennes : application à la programmation mi-convexe, mi-différentiable. C.R. Acad. Sc. Paris 284 A 959-961. Zbl0369.90095MR55 #6275
  16. A. AUSLENDER (1979) : Differentiable stability in non convex and non differentiable programming. Math. Programming, Study 10, 29-41. Zbl0403.90068MR80f:90109
  17. J. BAIR (1975) : Separation of two convex sets in convexity spaces and in straight line spaces. J. Math. Anal. Appl. 49 (3) 696-704. Zbl0302.52002MR50 #14152
  18. E.J. BALDER (1977) : An extension of duality-stability relations to non-convex optimization problems. SIAM J. control 15 (2) 329-343. Zbl0366.90103MR56 #10973
  19. M.L. BALINSKI - P. WOLFE (1975) : Nondifferential optimization. Math. Programming Study n°3, North Holland. Zbl0335.00010MR54 #14771
  20. J.M. BALL (1977) : Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal. 63 (4) 337-403. Zbl0368.73040MR57 #14788
  21. M.T. BANKS - M.Q. JACOBS (1970) : A differential calculus for multifunctions. J. Math. Anal. Appl. 29, 246-272. Zbl0191.43302MR42 #846
  22. J. BARANGER (1973) : Quelques résultats en optimisation non-convexe. Thèse, Grenoble et J. Math. Pures et Appl. 52 (4), 377-405. Zbl0274.46015MR52 #1260
  23. J. BARANGER - R. TEMAM (1974) : Problèmes d'optimisation non convexes dépendants d'un paramètre II, Analyse convexe et ses applications. Lecture - Notes in Economics and Math. Systems, N° 102, Springer-Verlag. Zbl0292.49003MR58 #2529
  24. J. BARANGER - R. TEMAM (1975) : Non convex optimization problems depending on a parameter. SIAM J. Control 13 (1) 146-152. Zbl0302.49003MR55 #3906
  25. M.S. BAZARAA (1973) : Geometry and resolution of duality gaps. Naval Res. Logistic Quaterly 20 (2), 357-366. Zbl0262.90056MR57 #18831
  26. G. BEER (1979) : Recession cones of non convex sets and increasing functions. Proc. Amer. Math. Soc. 73 (2), 228-232. Zbl0399.52002MR80b:52019
  27. A. BEN TAL (1977) : On generalized means and generalized convex functions. J. Optim. Th. and Appl. 21 (1) 1-14. Zbl0325.26007MR56 #552
  28. V.V. BERESNEF - B.N. PSENICNYI (1974) : The differential properties of minimum functions Z. Vycisl. Mat. i. Mat. Fiz. 14 (1974) 639-651, 812 MR 50 # 1735. Zbl0284.90069
  29. L.D. BERKOVITZ (1974) : Lower semi-continuity of integral functionals. Trans. Amer. Math. Soc. 192, 51-58. Zbl0294.49001MR50 #1079
  30. H. BERLIOCCHI - J.M. LASRY (1973) : Principe de Pontryagin pour des systèmes régis par une équation différentielle multivoque. C.R. Acad. Sci. Paris, 277 A 1103-1105. Zbl0282.49010MR50 #5580
  31. H. BERLIOCCHI - J.M. LASRY (1974) : Principe de Pontryagin pour des systèmes régis par une équation différentielle multivoque. Publications Math. de l'Univ. de Bordeaux (1973-1974) fasc. n° 2, 25-41. Zbl0357.49019
  32. D.P. BERTSEKAS - S.K. MITTER (1971) : Steepest descent for optimization problems with non differentiable cost functionals. in Proc. 5 th. annual Princeton Conf. on information and system sciences. 
  33. D.P. BERTSEKAS - S.K. MITTER (1973) : A descent numerical method for optimization problems with non differentiable cost functionals. SIAM J. Control 11 (4), 637-651. Zbl0243.49012MR48 #7592
  34. D.P. BERTSEKAS (1975) : Non differentiable optimization via approximation. Math. Progr. Study 3 1-25. Zbl0383.49025MR55 #13774
  35. M.F. BIDAUT-VERON (1973) : Théorèmes d'existence et d'existence "en général" d'un contrôle optimal pour des systèmes régis par des équations aux dérivées partielles non linéaires. Thèse, Paris. 
  36. R.L. BISHOP (1969) : Manifolds of negative curvature. Trans. Amer. Math. Soc. 145 1-49. Zbl0191.52002MR40 #4891
  37. F.S. de BLASI (1976) : On the differentiability of multifunctions. Pacific. J. Math. 66, 67-81. Zbl0348.58004MR56 #3874
  38. L.M. BLUMENTHAL (1953) : Theory and applications of distance geometry. The Clarendon Press, Oxford. Zbl0050.38502MR14,1009a
  39. V.G. BOLTYANSKII (1975) : The method of tents in the theory of extremal problems Russian Math. Surveys. 30 (3) 1-54. Zbl0334.49014
  40. J. BORWEIN (1977) : Weak local supportability and application to approximation (preprint) Dahlousie Univ. Halifax. 
  41. D.G. BOURGIN (1973) : Fixed point and min-max theorems. Pacific J. Math. 45 (2) 403-412. Zbl0275.55011MR49 #1512
  42. H. BREZIS - L. NIRENBERG - S. STAMPACCHIA (1972) : A remark on Ky Fan's minimax principle. Bull. Un. Mat. Ital. 6 (4), 293-300. Zbl0264.49013MR48 #2850
  43. F.E. BROWDER (1967) : A new generalization of the Schauder fixed point theorem. Math. Ann. 174 (1967) 285-290. Zbl0176.45203
  44. F.E. BROWDER (1973) : Normal solvability for nonlinear mappings into Banach spaces Bull. Amer. Math. Soc. 79, 328-350. 
  45. R.F. BROWN (1971) : The Lefschetz fixed point theorem. Scott, Foresman and C°, Glenview, Illinois. Zbl0216.19601MR44 #1023
  46. Yu. D. BURAGO - V.A. ZALGALLER (1977) : Convex sets in Riemannian spaces of non-negative curvature. Russian Math. Surveys 32 (3), 1-57. Zbl0397.53031
  47. V.W. BRYANT - R.J. WEBSTER (1972) : Convexity spaces I. Basic properties. J. Math. Anal. Appl. 37 - 206-213, idem II Separation 43 (1973) 321-327, idem III Dimension 57 (2) (1977) 382-392. Zbl0259.52001
  48. C. CASTAING - M. VALADIER (1977) : Convex analysis and measurable multifunctions. Lectures Notes in Math n° 580. Springer Verlag. New-York. Zbl0346.46038MR57 #7169
  49. L. CESARI (1974) : An existence theorem without convexity conditions. SIAM J. Control 12 (2) 319-331. Zbl0255.49008MR52 #4060
  50. D. CHENAIS (1975) : On the existence of a solution in a domain identification problem. J. Math. Analysis Appl. 52 (2) 189-219. Zbl0317.49005MR52 #6526
  51. D. CHENAIS (1975) : Un ensemble de variétés à bord lipschitziennes dans ℝn : compacité, théorème de prolongement dans certains espaces de Sobolev. C.R. Acad. Sc. Paris 280 A 1145-1147. Zbl0296.46039MR54 #11763
  52. Y. CHERRUAULT (1970) : Minimization de fonctionnelles non convexes. Rend. Mat. VI série 3 (1971) 777-785, MR 44 # 7715. Zbl0237.49029
  53. G. CHICHILNISKY (1977) : Nonlinear functional analysis and optimal economic growth J. Math. Anal. Appl. 61 (2) 504-520. Zbl0363.90028MR57 #5004
  54. F.H. CLARKE (1975) : Generalized gradients and applications. Trans. Amer. Math. Soc. 205, 247-262. Zbl0307.26012MR51 #3373
  55. F.H. CLARKE (1975) : The Euler-Lagrange Differential inclusion. J. Diff. Eq. 19, 80-90. Zbl0323.49021MR52 #9033
  56. F.H. CLARKE (1975) : Admissible relaxation in variational and control problems. J. Math. Anal. and Appl. 51, 557-576. Zbl0326.49031MR53 #11448
  57. F.H. CLARKE (1976) : Optimal solutions to differential inclusions. J. Optim. Th. Appl. 19 (3) 469-478. Zbl0307.49042MR54 #13667
  58. F.H. CLARKE (1976) : A new approach to Lagrange multipliers. Math. Operations Research 1, 165-174. Zbl0404.90100MR54 #2209
  59. F.H. CLARKE (1977) : Multiple integrals of Lipschitz functions in the calculus of variations. Proc. Amer. Math. Soc. 64 (2) 260-264. Zbl0411.49015MR56 #9443
  60. L. COLLATZ (1974) : Different applications of convex and non convex optimization, especially to differential equations, in “Spectral theory and differential equations”. W.N. Everitt ed. Lectures Notes in Math. n° 448, p. 112-125. Zbl0319.49023MR53 #2372
  61. B. CORNET — J.M. LASRY (1976) : Un théorème de surjectivité pour une procédure de planification. C.R. Acad. Sc. Paris 282 (23) A 1375-1378. Zbl0347.90020MR54 #4586
  62. J.P. CROUZEIX (1976) : Conjuguay in quasi-convex analysis. Proceedings conference Murat le Quaire. Lectures Notes in Economies and Math. Syst. n° 144. Zbl0362.90096
  63. J.P. CROUZEIX (1977) : Contribution à l'étude des fonctions quasiconvexes. Thèse, Univ. Clermont-Ferrand II. MR58 #4332
  64. J.P. CROUZEIX (1976) : Dualité quasi-convexe. Séminaire d'analyse numérique, Univ. de Clermont. 
  65. J.W. DANIEL (1971) : The approximate minimization of functionals. Prentice Hall, Englewood Cliffs N.Y. Zbl0223.65014MR42 #7279
  66. I.I. DANILJUK (1972) : On integral functionals with a variable domain of integration. Proc. Steklov Inst. Math. 118, Amer. Math. Soc. Providence (1976). Zbl0325.35002
  67. L. DANZER, B. GRÜNBAUM, V. KLEE (1963) : Helly's theorem and its relatives. Proc. Symp. Pure Math. 7, 101-180. Amer. Math. Soc. Providence. Zbl0132.17401MR28 #524
  68. G. DANTZIG — J. FOLKMAN — N. SHAPIRO (1967) : On the continuity of the minimum set of continuous fonctions. Journ. Math. Anal. Appl. 17, 519-548. Zbl0153.49201MR34 #7241
  69. A. DELEANU (1959) : Théorie des points fixes sur les rétractes de voisinage des espaces convexoïdes. Bull. Soc. Math. France 87, 235-243. Zbl0093.36801MR26 #763
  70. E. DIERKER (1974) : Topological methods in Walrasian economics. Lect. notes in Economics n° 92, Springer Verlag, Berlin. Zbl0285.90005MR51 #14902
  71. J. DIESTEL — J.J. UHL (1977) : Vector measures. Math. Survey n° 15, Amer. Math. Soc., Providence, Rhode Island. Zbl0369.46039MR56 #12216
  72. F. DI GUGLIELMO (1976) : Estimates of the duality gap for discrete optimization, Séminaire Analyse convexe, Montpellier 3-1, 3-27 et C.R. Acad. Sc. Paris 282, 883-886. Zbl0356.90041MR58 #32928
  73. S. DOLECKI, S. KURCYUSZ (1976) : Convexité généralisée et optimisation. C.R. Acad. Sci. Paris 238, A 91-94. Zbl0341.49005MR54 #12209
  74. S. DOLECKI, S. KURCYUSZ (1978) : On Φ-convexity in extremal problems. SIAM J. Control and Opt. 16 (2) 277-300. Zbl0397.46013MR57 #18824
  75. S. DUBUC (1960) : Topological convex spaces. Ph. D. THESIS, Cornell Univ. N.Y. 
  76. M. EDELSTEIN (1966) : Farthest points of sets in uniformly convex Banach spaces. J. London Math. Soc. 43, 375-377. Zbl0183.40403
  77. J. EISENFELD — V. LAKSHMIKANTHAM (1976) : On a measure of non convexity and applications. Technical report n° 26. Univ. of Texas at Arlington. The Yokohama Math. J. 24 (1-2), 133-140. Zbl0361.34051MR54 #13657
  78. I. EKELAND (1974) : On the variational principle. J. Math. Anal. and Appl. 47 (2) ; 324-353. Zbl0286.49015MR49 #11344
  79. I. EKELAND (1979) : Nonconvex minimization problems. Bull. Amer. Math. Soc. (new series) 1 (3) 443-474. Zbl0441.49011MR80h:49007
  80. I. EKELAND — G. LEBOURG (1975) : Sous gradients approchés et applications. C.R. Acad. Sc. Paris 281 A 219-222. Zbl0321.49031MR52 #1297
  81. I. EKELAND — G. LEBOURG (1976) : Generic Frechet differentiability and perturbed optimization problems in Banach spaces. Trans. Amer. Math. Soc. 224 (2) 193-216. Zbl0313.46017MR55 #4254
  82. I. EKELAND — R. TEMAM (1974) : Analyse convexe et problèmes variationnels. Dunod-Gauthier-Villars, Paris. Edité en anglais par North Holland avec un appendice. Zbl0281.49001MR57 #3931a
  83. I. EKELAND — M. VALADIER (1971) : Représentation of set-valued mappings. J. Math. Anal. Appl. 35, 621-629. Zbl0246.54018MR43 #6396
  84. J.P. EVANS — F.J. GOULD (1970) : Stability in nonlinear programming. Operation Research 18, 107-118. Zbl0232.90057MR41 #9573
  85. K. FAN (1953) : Minimax theorems. Proc. Nat. Acad. Sci. 39, 42-47. Zbl0050.06501MR14,1109f
  86. A.V. FIACCO (1976) : Sensitivity analysis for nonlinear programming using penalty methods. Math. Program. 10 287-311. Zbl0357.90064MR55 #7410
  87. F. FICHEUX - G.S. RUBINSTEIN (1975) : Préordres quasi-convexes (en russe) Optimizacija 16 (33), 127-146, Zentralblatt 46012 N 327. Zbl0327.46012MR55 #13323
  88. A. F. FILIPPOV (1967) : Classical solutions of differential equations with multivalued right hand side. SIAM J. Control 5, 609-621. MR36 #4047
  89. A.F. FILIPPOV (1971) : On the existence of solutions of multivalued differential equations. Math. Zametki 10, 307-313. Zbl0254.34004MR45 #7142
  90. A.L. FRADKOV (1976) : Duality theorems for certain non convex extremal problems Siberian Math J. 14 (2) ; 247-263. Zbl0269.49008
  91. S. GAUTIER (1979) : Différentiabilité des multiapplications. Publications Math. de Pau. 
  92. J. GAUVIN - J.W. TOLLE (1977) : Differential stability in nonlinear programming. SIAM J. Control 15 (2), 294-311. Zbl0374.90062MR55 #14215
  93. J.S. GIBSON - I.G. CLARK (1977) : Sensitivity analysis for a class of evolution equations. J. Math. Anal. Appl. 58 (1), 22-31. Zbl0393.34036MR56 #3426
  94. C. GODET - THOBIE (1975) : Multimesures et multimesures de transition. Thèse, Montpellier. Zbl0344.28003
  95. A.A. GOLDSTEIN (1977) : Optimization of Lipschitz continuous functions. Math. Programming 13 (1) 38-48. Zbl0394.90088MR56 #1705
  96. G.S. GOODMAN - J. HOFFMANN - JØRGENSEN (1969) : Support functions and the function space embedding of infinite dimensional convex sets. Core discussion Papers, Louvain. 
  97. W. B. GORDON (1971) : A theorem on the existence of periodic solutions to Hamiltonian systems with convex potential. J. Diff. Eq. 10 (2), 324-335. Zbl0231.35006MR45 #1200
  98. W.B. GORDON (1972) : Convex functions and harmonic maps. Proc. Amer. Math. Soc. 33 (2) 433-437. Zbl0216.42801MR45 #1075
  99. W.B. GORDON (1974) : The existence of geodesics joining two given points. J. Diff. Geom. 9, 443-450. Zbl0281.53035MR49 #4032
  100. M.J. GREENBERG - W.P. PIERSKALLA (1975) : Stability theorems for infinitely constrained mathematical programs. J. Optim. Th. Appl. 16 (5/6) 409-428. Zbl0291.90062MR56 #14719
  101. D. GROMOLL (1970) : Manifolds of non negative curvature. Actes Congrès Intern. Math. t.2, 177-180. Nice. Zbl0234.53044MR54 #11234
  102. R. GUESNERIE (1969) : Optimum de Pareto et ensembles de production non convexes. Bull. Math. Economiques 2, 31-60. 
  103. J. GWINNER (1977) : Closed images of convex multivalued mappings in linear topological spaces with applications. J. Math. Anal. Appl. 60, 75-86. Zbl0373.46012MR57 #13447
  104. H. HALKIN (1976) : Mathematical programming without differentiability. In “Calculus of variations and control theory”, edited by D.L. Russel, Academic Press. Zbl0355.90059MR55 #8927
  105. B. HALPERN - G. BERGMAN (1968) : A fixed point theorem for inward and outward maps. Trans. Amer. Math. Soc. 130, 353-358. Zbl0153.45602MR36 #4397
  106. B. HALPERN (1970) : Fixed point theorems for set-valued maps in infinite dimensional spaces. Math. Ann. 189, 87-98. Zbl0191.14701MR42 #8357
  107. D.J. HARTFIELD, G.L. CURRY (1974) : Concerning the solution vector for parameter programming problems. SIAM J. Appl. Math. 26, 294-296. MR 48 # 10503. Zbl0284.90075
  108. H. HERMES (1969) : Existence and properties of solutions of xє R(t,x). SIAM, Study Applied Math 5, 188-193. 
  109. H. HERMES (1970) : The generalized differential equation xєR(t,x). Advances in Math. 4, 149-169. Zbl0191.38803MR40 #5939
  110. W. HILDENBRAND, D. SCHMEIDLER, S. ZAMIR (1973) : Existence of approximate equilibria and cores Econometrica 41 (1973) 1159-1166. Zbl0298.90013
  111. J.B. HIRIART-URRUTY (1976) : Gradients généralisés de fonctions marginales. C.R. Acad. Sci. Paris 283, 333-335., SIAM J. Control Opt. 16 (2) (1978) 301-316. Zbl0385.90099
  112. J.B. HIRIART-URRUTY (1978) : Conditions nécessaires d'optimalité pour un programme stochastique avec recours. SIAM J. Control and Opt. 16 (2) 317-329. Zbl0382.62072MR58 #15158
  113. HOANG TUY (1974) : On an axiomatic for extremal problems and first order necessary conditions. Soviet Math. Dokl. 15 (3) 978-983. Zbl0333.49019
  114. HOANG TUY (1974) : On a general minimax principle. Soviet Math. Doklady 15 (6) 1689-1693. Zbl0314.90088
  115. L. HORMANDER (1954) : Sur la fonction d'appui des ensembles convexes dans un espace localement convexe. Ark. Mat. 3, 181-186. MR 16-720. Zbl0064.10504MR16,831e
  116. R.E. HUFF — P.D. MORRIS (1976) : Geometric characterization of the Radon-Nikodym property in Banach spaces. Studia Math. 56 (2) 157-164. Zbl0351.46011MR54 #897
  117. M. HUKUHARA (1967) : Intégration des applications mesurables dont la valeur est un compact convexe. Funk. Ekvac. 10, 205-223. Zbl0161.24701MR37 #2092
  118. F.N. HUGGINS (1977) ; Bounded slope variationand generalized convexity. Proc. AMS 65 (1), 65-69. Zbl0374.26009MR57 #6326
  119. A.D. IOFFE (1977) : Sur la semi-continuité des fonctionnelles intégrales. C.R. Acad. Sc. Paris 284, 807-809. Zbl0348.49009MR55 #3910
  120. A.D. IOFFE (1977) : On lower semi-continuity of integral functionals I, II, SIAM. J. Control Opt. 15 (4) 521-538, 15 (6), 991-1001. Zbl0361.46037MR58 #30610a
  121. R. JANIN (1974) : Sur la dualité et la sensibilité dans les problèmes de programmation mathématique. Thèse, Paris et J. Math. Anal. & Appl.60(3) (1977) 631-657. 
  122. R. JANIN (1976) : Sensitivity for non convex optimization problems in convex analysis and its applications. Lectures notes in Economics and Math. Systems. n° 144, Springer Verlag. Zbl0359.90071
  123. C. JOURON (1975) : Etude des conditions nécessaires d'optimalisé pour un problème d'optimisation non convexe. C.R. Acad. Sc. Paris 281 (23), 1031-1034. Zbl0317.49021MR52 #9038
  124. H. KACZINSKI — C. OLECH (1974) : Existence of solutions of orientor fields with nonconvex right hand side, Ann. Polon. Math. 29, 61-66. Zbl0285.34008
  125. W. KECS (1974) : On a certain generalization of Legendre's condition in the calculus of variations to integrals depending on higher order derivatives. Studia. Cerc. Math. 26, 32-52 MR 50 # 14418. Zbl0279.49024MR50 #14418
  126. W.A. KIRK (1976) : Caristi's fixed point theorem and metric convexity (preprint). Zbl0353.53041MR55 #9061
  127. V. KLEE (1951) : Convex sets in linear spaces Duke Math. J. 18, 443-466. Zbl0042.36201MR13,354f
  128. H. KNESER (1952) : Convexe Raume, Archiv. der Math. 3, 198-206. Zbl0048.08601MR14,478e
  129. G. KNOWLES (1977) : Some remarks on infinite dimentional nonlinear control without convexity. SIAM J. contol and Optim. 15 (5), 830-840. Zbl0362.49010MR56 #9359
  130. J.M. LASRY (1975) : Communication personnelle. 
  131. J.M. LASRY (1976) : Structure de l'ensemble des solutions d'une équation différentielle multivoque. Conséquences. Journées de contrôle, Metz, mai 76. 
  132. J.M. LASRY — R. ROBERT (1976) : Analyse non linéaire multivoque. Cahiers de Math. de la décision Univ. Paris IX. n° 7611. Zbl0538.03053
  133. M. LASSAK (1977) : On metric B-convexity for which diameters of any set and its hull are equal. Bull. Acad. Pol. Sc. 25 (10), 969-975. Zbl0379.52010MR57 #1271
  134. G. LEBOURG (1975) : Valeur moyenne pour gradient généralisé. C.R. Acad. Sc. Paris ; 281, 795-797. Zbl0317.46034MR52 #8934
  135. G. LEBOURG (1977) : Generic differentiability of Lipschitzian functions. Cahiers de Math. de la décision. Univ. Paris Dauphine, n° 7704. Zbl0435.46031
  136. J. LERAY (1945) : Sur la forme des espaces topologiques et sur les points fixes des représentations. J. Math. Pures Appl. 24, 95-167. Zbl0060.40703MR7,468e
  137. J. LERAY (1959) : Théorie des points fixes, indice total et nombre de Lefschetz. Bull. Soc. Math. de France 87, 221-233. Zbl0093.36702MR26 #762
  138. P. LEVINE, J.C. POMEROL (1976) : C-Closed mappings and Kuhn-Tucker vectors in convex programming. Core Discussion paper n° 7620. Louvain. 
  139. P. LEVINE, J.C. POMEROL (1978) : Quelques extensions des théorèmes "inf-sup", C.R. Acad. Sci. Paris 287, A 565-567. Zbl0395.49024MR58 #26062
  140. E.S. LEVITIN (1974) : The differential properties of the optimal value of parametric mathematical programming problems. Soviet Math. Dokl. 15, 603-608. MR 50 # 1086. Zbl0309.90048MR50 #1086
  141. C. LEMARECHAL (1975) : Note on an extension of Davidon's method to non-differentiable functions. Math. Progr. Study 3, 110-126. 
  142. A. LEW (1975) : Stability, prediction-correction and dynamic programming. J. Optim. Th. and Appl. 17 (314), 229-238. Zbl0298.49013MR53 #9006
  143. C. LOBRY (1972) : Aspects qualitatifs de la théorie des équations différentielles multivoques. Séminaire Math. Appl. Bordeaux, exp. n°3, Publications Univ. Bordeaux 72-73. 
  144. D.G. MAHAJAN, M.N. VARTAK (1977) : Generalization of some duality theorems in non-linear programming. Math. Programm. 12 (3) 392-405. Zbl0358.90059MR56 #17828
  145. C. MALIVERT (1977) : Optimisation sur une variété anguleuse ou un fermé non convexe. Thèse 3ème cycle, Pau. 
  146. O.L. MANGASARIAN (1965) : Pseudo-convex functions. J. SIAM Control 3, 281-290. Zbl0138.15702MR32 #9062
  147. O.L. MANGASARIAN (1969) : Nonlinear programming. Mc Graw Hill, New-York. Zbl0194.20201
  148. O.L. MANGASARIAN (1975) : Second and higher order duality in nonlinear programming. J. Math. Anal. Appl. 51 (3), 557-576. Zbl0313.90052MR51 #14995
  149. M. MARTELLI — A. VIGNOLI (1974) : On differentiability of multivalued maps. Bull. Un. Math. Ital. (4) 10, 701-702. Zbl0311.46029MR51 #6417
  150. D.H. MARTIN (1975) : On the continuity of the maximum in parametric linear programming. J. Optim. Th. and Appl. 17 (3/4) 205-210. Zbl0298.90041MR52 #7528
  151. R.H. MARTIN Jr (1976) : Nonlinear operators and differential equations in Banach spaces. Wiley-Interscience, New-York. Zbl0333.47023
  152. A. MAS COLELL (1979) : A selection theorem for open graph correspondances with starshaped valued. J. Math. Anal. Appl.68 (1), 273-275. Zbl0497.54011MR80e:54059
  153. H. MASSAM — S. ZLOBEC (1974) : Various definitions of the derivative in mathematical programming, Math. Pro. 7 (2), 144-161. Zbl0296.90042MR50 #3066
  154. E. MAZET (1974) : Problèmes relatifs aux applications harmoniques. Thèse, Paris. 
  155. K. MENGER (1928) : Untersuchungen über allgemenie Metrik. Math. Annalen 100, 75-163. Zbl54.0622.02JFM54.0622.02
  156. P. MEREAU — P.G. PAQUET (1973) : The use of pseudo-convexity and quasi convexity in sufficient conditions for global constrained extrema. Int. J. Control (1) (18) 831-838 MR 48 # 10505. Zbl0271.90040MR48 #10505
  157. P. MICHEL (1973) : Problème des inégalités. Application à la programmation et au contrôle optimal. Bull. Soc. Math. de France 101, 413-439. Zbl0295.90033MR49 #11350
  158. M. MICHEL (1974) : Problèmes des inégalités et application à la programmation dans le cas où l'espace d'arrivée est de dimension finie. C.R. Acad. Sc. Paris 278, 339-391. MR52 #4067
  159. S. MITETELU (1976) : Kuhn-Tucker conditions for non-linear programming with quasi-convex constraints. Revue Roum. Math. Pures Appl. 21 (7) 903-909. Zbl0351.90058
  160. J.J. MOREAU (1963) : Fonctions à valeurs dans [-∞, +∞] ; notions algébriques, Faculté des Sciences de Montpellier, séminaires de Math. (multigraphié). Zbl0137.31304MR28 #2427
  161. C.B. MORREY (1966) : Multiple integrals in the calculus of variations. Springer-Verlag. New-York. Zbl0142.38701MR34 #2380
  162. F. MURAT — J. SIMON (1974) : Quelques résultats sur le contrôle par un domaine géométrique. Laboratoire d'analyse numérique. Univ. Paris VI. 
  163. F. MURAT — J. SIMON (1976) : Sur le contrôle par un domaine géométrique. Laboratoire d'analyse numérique. Univ. Paris VI. 
  164. D. NETZER — U. PASSY (1975) : A note on the maximum of quasi-concave functions. J. Optim. Th. Appl. 16 (5/6) 565-570. Zbl0291.90060MR52 #10041
  165. C. OLECH (1975) : Existence theory in optimal control problems. The underlying ideas. Proc. Intern. Conf. in differential Equations. Los Angeles (1974) Academic Press, N.Y. Zbl0353.49013
  166. C. OLECH (1976) : Weak lower semi-continuity of integral functionals. J. Optim. Th. and Appl. 19 (1) 3-17. Zbl0305.49019MR55 #1188
  167. C. OLECH (1969) : Existence theorems for optimal control problems involving multiple integrals. J. Diff. Eq. 6, 512-526 MR 39 # 7488. Zbl0184.19404MR39 #7488
  168. C. OLECH (1975) : Existence of solutions of nonconvex orientor fields. Boll. Univ. Mat. Ital. 11 (4) fasc. 3 suppl. 189-197. Zbl0322.34002MR52 #15174
  169. R. PALLU de la BARRIERE (1974) : Fonctions sous-linéarisables et principe de Pontryagin, Publications Math. Univ. de Bordeaux I (1973-1974) (3), 65-72. 
  170. B. PALMERIO - A. DERVIAUX (1974): Identification de domaines et problèmes de frontière libre. Thèse 3ème cycle. Nice. 
  171. B. PALMERIO - A. DERVIAUX (1975) : Une formule de Hadamard dans des problèmes d'identification de domaine. C.R. Acad. Sc. Paris 280 A, 1697-1700. Zbl0303.35065MR52 #7126
  172. T. PARTHASARATHY, T.E.S. RAGHAVAN (1971) : Some topics in two-person games, Amer. Elsevier, New-York. Zbl0225.90049MR43 #2996
  173. J.P. PENOT (1974) : Sous-différentiels de fonctions numériques non convexes. C.R. Acad. Sc. Paris 278 A 1553-1555. Zbl0318.46055MR50 #5464
  174. J.P. PENOT (1974) : Calcul sous-différentiel et optimisation. Publications Math. Univ. de Pau II 1-40 et J. Functional Analysis, 27 (2) (1978) 248-276. Zbl0404.90078
  175. J.P. PENOT (1978) : Utilisation des sous-différentiels généralisés en optimisation. 1er colloque AFCET - S.M.F. tome 3, 69-85. Zbl0483.49023
  176. J.P. PENOT (1979) : The use of generalized subdifferential calculus in optimization theory. Third Symp. on Operations Research, Mannheim (1978), Verlag Athenäum, Hain, Scriptor, Hanstein. Zbl0409.26003
  177. D.W. PETERSON (1974) : On sensitivity in optimal control problems. J. Optim. Th. and Appl. 13 (1), 56-73. Zbl0255.49019MR49 #3640
  178. G. PIANIGIANI (1977) : On the fundamental theory of multivalued differential equations. J. Diff. Equat. 25 (I), 30-38. Zbl0398.34017MR58 #12638
  179. A. PLIS (1963) : Trajectories and quasi trajectories of an orientor field. Bull. Acad. Polon. Sci. Mat. Astronom. Phys. 11, 369-370. Zbl0124.29404MR27 #5014
  180. P. PUCCI (1977) : Sulla determinazione di tute le soluzione di un campo di orientori non convesso. Boll. Un. Mat. Ital. 14 (5) B - 393-401. Zbl0371.34002MR57 #1244
  181. J. PONSTEIN (1967) : Seven kinds of convexity. SIAM Review 9 (1), 115-119. Zbl0164.06501MR35 #4813
  182. B.N. PSHENICHNYI (1971) : Necessary conditions for an extremum. Pure and Applied Math. Marcel Dekker, New-York. Zbl0212.23902MR43 #2585
  183. T. RADER (1973) : Absolutely continuous constrained miximizers. J. Optim. Th. and Appl. 12 (2), 107-128. Zbl0248.90060MR48 #13269
  184. H. RADSTROM (1952) : An embedding theorem for spaces of convex sets. Proc. Amer. Math. Soc. 3, 165-169. Zbl0046.33304MR13,659c
  185. C. RAFFIN (1970) : Sur les programmes convexes définis dans des espaces vectoriels topologiques. Annales Inst. Fourier 20 (1), 457-491. Zbl0195.49601MR42 #1527
  186. S. REICH (1977) : Approximate selections, best approximations, fixed points and invariant sets (preprint). 
  187. A.W. ROBERTS-D.E. VARBERG (1973) : Convex functions. Academic Press, New-York. Zbl0271.26009MR56 #1201
  188. A.W. ROBERTS-D.E. VARBERG (1973) : Functions of bounded convexity, Bull. Amer. Math. Soc. 75, 568-572. Zbl0176.01204MR39 #380
  189. S.M. ROBINSON (1975) : A characterization of stability in linear programming. MRC Techn. Report n° 1542, Univ. of Wisconsin. Madison. 
  190. S.M. ROBINSON-R.H. DAY (1974) : A sufficient condition for continuity of optimal sets in mathematical programming. J. Math. Anal. Appl. 45, 506-511, MR 48 # 10518. Zbl0291.90063MR48 #10518
  191. R.T. ROCKAFELLAR (1970) : Convex analysis. Princeton Math. Series Princeton, Univ. Press. Princeton, New-York. Zbl0193.18401MR43 #445
  192. R.T. ROCKAFELLAR (1974) : Augmented Lagrange multiplier functions and duality in non-convex programming. SIAM J. Control. 12 (2), 268-285. Zbl0257.90046MR52 #5040
  193. R.T. ROCKAFELLAR (1975) : Existence theorems for general control problems of Bolza and Lagrange. Advances in Math. 15, 312-315. Zbl0319.49001MR51 #1526
  194. A.M. ROUS (1971) : Problèmes de relaxation pour les équations différentielles à commandes dans les espaces de Banach. D.E.A. Univ. Montpellier, Publication N° 102. 
  195. B. ROUSSELET (1976) : Etude de la régularité de valeurs propres par rapport à des déformations bilipschitziennes du domaine géométrique. C.R. Acad. Sc. Paris 283 (7), 507-510. Zbl0355.65081MR55 #895
  196. G.S. RUBINSTEIN (1973): Caractérisation d'une classe de fonctions convexes. Optimizacija 9 (26), 165-180. Zbl0304.90091MR51 #8849
  197. J. SAINT-PIERRE (1974) : Somme d'un compact et d'un fermé localement compact dans un groupe topologique. Séminaire d'Analyse convexe, Montpellier, exposé N° 17. Zbl0335.22001MR58 #22375
  198. S. SCHAIBLE (1977) : Second order characterization of pseudo-convex quadratic function. J. Optim. Th. Appl. 21 (1) 15-26. Zbl0326.26004MR55 #5818
  199. M.R. SERTEL (1975) : The fundamental continuity theory of optimization on a compact space I. J. Optim. Th. and Appl. 16 (5/6) 549-558. Zbl0291.49007MR52 #9032
  200. E.J. Mc. SHANE (1967) : Relaxed controls and variational problems. SIAM J. Control 5, 438-485. Zbl0153.13104MR36 #2033
  201. E. SILVERMAN (1973) : A necessary condition in the calculus of variations. Proc. Amer. Math. Soc. 37 462-464 MR 47 # 7555. Zbl0261.49020MR47 #7555
  202. E. SILVERMAN (1973) : Strong quasi-convexity. Pacific J. Math. 46 549-554 MR 48 # 9488. Zbl0252.49005MR48 #9488
  203. A.D. SOLOMON (1975) : On parameter dependance of the solution to an extremal problem. J. Optim. Th. and Appl. 17 (1/2), 163-168. Zbl0292.49025MR52 #4069
  204. J. STOER, C. WITZGALL (1970) : Convexity and optimization in finite dimensions I., Springer Verlag, Berlin. Zbl0203.52203MR44 #3707
  205. M.H. STONE (1949) : Postulates for the barycentric calculus. Annali. di. Mat. (4) 29, 25-30, MR 12, 45. Zbl0037.25002MR12,45h
  206. S. SZUFLA (1973) : Solutions sets of nonlinear equations. Bull. Acad. Pol. Sc. 21 (11) 971-976. Zbl0272.34086MR49 #9698
  207. S. SZUFLA (1977) : On the structure of solution sets of differential and integral equations in Banach Spaces. Annales Polon. Math. 34, 165-177. Zbl0384.34038MR57 #3553
  208. S. TAGAWA (1974) : Generalized convexities of continuous functions and their application to mathematical programming. Bull. Math. Stat. 16 (1/2), 115-121. Zbl0295.90034MR51 #7624
  209. L. THIBAULT (1976) : Problème de Bolza dans un espace de Banach séparable. Séminaire d'analyse convexe de Montpellier et C.R. Acad. Sc. Paris 282 A 1303-1306. Zbl0357.49018MR55 #8931
  210. L. THIBAULT (1976) : Propriétés des sous-différentiels de fonctions localement lipschitziennes définies sur un espace de Banach séparable. Applications. Thèse 3ème cycle. Montpellier. Zbl0343.46030MR55 #1378
  211. L. THIBAULT : Subdifferentials of Compactly Lipschitzian Vector-Valued Functions (to appear in Ann. Mat. Pura Appl.). Zbl0486.46037
  212. L. THIBAULT : Mathematical Programming and Optimal Control Problems Defined by Compactly Lipschitzian Mappings (to appear). 
  213. J.P. TOLAND (1976) : A duality principle for non-convex optimization and the calculus of variations. Report n° 77 Fluid Mech. Research Inst. Univ. of Essex. 
  214. J.F. TOLAND (1977) : On the stability of rotating heavy chains idem n° 82. 
  215. J.F. TOLAND (1978) : Duality in nonconvex optimization. idem N° 78 et J. Math. Anal. Appl. 66 (2), 399-414. Zbl0403.90066MR80a:49025
  216. P.P. VARIAYA (1967) : On the trajectories of a differential system in Mathematical theory of control, A.V. Balakrishnam, L.W. Neustadt, ed. Acad. Press, New-York. 115-128. Zbl0235.49009MR40 #4561
  217. G. VIDOSSICH (1971) : On the structure of the set of solutions of nonlinear equations. J. Math. Anal. Appl. 34, 502-617. MR44 #875
  218. J. WARGA (1962) : Relaxed variational problems. J. Math. Anal. Appl. 4, 111-128. Zbl0102.31801MR25 #5415a
  219. J. WARGA (1976) : Derivative containers, inverse functions and controllability in calculus of variations and control theory, edited by D.L. Russel, Academic Press, New-York. Zbl0355.26004
  220. Ja. I. ZABOTIN (1973) : Conditions for the extremum of a functional in the presence of constraints. Kibernetika (Kiev) (6), 65-70 MR 50 # 1723. Zbl0273.90051MR50 #1723
  221. V. ZIRLER (1973) : On some extremal problems in Banach spaces. Math. Scand. 32, 214-224. Zbl0269.46014MR49 #11217
  222. J.P. ZOLESIO (1976) : An optimal design procedure for optimal control support. In Convex analysis and its applications, Lectures notes in economics and Math. systems n° 144, p 207-219. Zbl0358.49004MR58 #23892
  223. J.P. ZOLESIO (1979) : Identification de domaines par déformations. Thèse, Nice. 

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