Introduction to the volume

Penot, Jean-Paul

Analyse non convexe (Pau, 1977), Mémoires de la Société Mathématique de France, no. 60 (1979), pp. 7-24.

Zbl

DOI : 10.24033/msmf.257

@incollection{MSMF_1979__60__7_0,
     author = {Penot, Jean-Paul},
     title = {Introduction to the volume},
     booktitle = {Analyse non convexe (Pau, 1977)},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     pages = {7--24},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {60},
     year = {1979},
     doi = {10.24033/msmf.257},
     zbl = {0412.90058},
     url = {http://archive.numdam.org/articles/10.24033/msmf.257/}
}

TY  - CHAP
AU  - Penot, Jean-Paul
TI  - Introduction to the volume
BT  - Analyse non convexe (Pau, 1977)
AU  - Collectif
T3  - Mémoires de la Société Mathématique de France
PY  - 1979
SP  - 7
EP  - 24
IS  - 60
PB  - Société mathématique de France
UR  - http://archive.numdam.org/articles/10.24033/msmf.257/
DO  - 10.24033/msmf.257
ID  - MSMF_1979__60__7_0
ER  -

%0 Book Section
%A Penot, Jean-Paul
%T Introduction to the volume
%B Analyse non convexe (Pau, 1977)
%A Collectif
%S Mémoires de la Société Mathématique de France
%D 1979
%P 7-24
%N 60
%I Société mathématique de France
%U http://archive.numdam.org/articles/10.24033/msmf.257/
%R 10.24033/msmf.257
%F MSMF_1979__60__7_0

Penot, Jean-Paul. Introduction to the volume, dans Analyse non convexe (Pau, 1977), Mémoires de la Société Mathématique de France, no. 60 (1979), pp. 7-24. doi : 10.24033/msmf.257. http://archive.numdam.org/articles/10.24033/msmf.257/

Bibliographie
Cité par

J.C. Aggeri : Isomorphisme d'un cône convexe abstrait à un cône fonctionnel. J. Math. Pures et Appl. 52 (4) (1973) 443-451. | MR | Zbl

S. Alexander - R.L. Bishop (1974) : Convex supporting domains on spheres. Illinois J. Math. 18, 37-47. | MR | Zbl

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. | MR | Zbl

P. Antoine (1976) : Conditions pour un minimum local d'une fonction différentiable. Pub. U.E.R. Math. Univ. Lille I N° 97.

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. | MR | Zbl

A.A. Antoziewicz - A. Cellina (1975) : Continuous selections and differential relations. J. Diff. Eq. 19, 386-398. | MR | Zbl

K.J. Arrow - A. Enthoven (1961) : Quasiconcave programming. Econometrica. 29, 779-800. | MR | Zbl

E. Asplund (1966) : Farthest points in reflexive locally uniformly rotund Banach spaces. Israel J. Math. 4, 213-216. | MR | Zbl

J-P. Aubin (1974) : Analyse convexe et ses applications. Comptes-rendus, Lectures Notes in Economics and Mathematical Systems n° 102, Springer-Verlag. | MR | Zbl

J-P. Aubin (1979) : Mathematical methods of game and economic theory. North Holland, Amsterdam. | MR | Zbl

J-P. Aubin - F. Clarke (1976) : Monotone trajectories of non-convex multivalued dynamical systems. MRC Tech. Report. Univ. of Wisconsin, Madison.

J-P. Aubin - I. Ekeland (1976) : Estimates of the duality gap in nonconvex optimization, Math. of Operations Research 1, 225-245. | MR | Zbl

R.J. Aumann - M. Perles (1965) : A variational problem arising in economics. J. Math. Anal. Appl. 11, 488-503. | MR | Zbl

A. Auslender (1976) : Convex analysis and its applications. Proceedings Conf. Murat le Quaire. Lecture Notes in Economics and Mathematical systems n°144. | MR | Zbl

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. | MR | Zbl

A. Auslender (1979) : Differentiable stability in non convex and non differentiable programming. Math. Programming, Study 10, 29-41. | MR | Zbl

J. Bair (1975) : Separation of two convex sets in convexity spaces and in straight line spaces. J. Math. Anal. Appl. 49 (3) 696-704. | MR | Zbl

E.J. Balder (1977) : An extension of duality-stability relations to non-convex optimization problems. SIAM J. control 15 (2) 329-343. | MR | Zbl

M.L. Balinski - P. Wolfe (1975) : Nondifferential optimization. Math. Programming Study n°3, North Holland. | MR | Zbl

J.M. Ball (1977) : Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal. 63 (4) 337-403. | MR | Zbl

M.T. Banks - M.Q. Jacobs (1970) : A differential calculus for multifunctions. J. Math. Anal. Appl. 29, 246-272. | MR | Zbl

J. Baranger (1973) : Quelques résultats en optimisation non-convexe. Thèse, Grenoble et J. Math. Pures et Appl. 52 (4), 377-405. | MR | Zbl

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. | MR | Zbl

J. Baranger - R. Temam (1975) : Non convex optimization problems depending on a parameter. SIAM J. Control 13 (1) 146-152. | MR | Zbl

M.S. Bazaraa (1973) : Geometry and resolution of duality gaps. Naval Res. Logistic Quaterly 20 (2), 357-366. | MR | Zbl

G. Beer (1979) : Recession cones of non convex sets and increasing functions. Proc. Amer. Math. Soc. 73 (2), 228-232. | MR | Zbl

A. Ben Tal (1977) : On generalized means and generalized convex functions. J. Optim. Th. and Appl. 21 (1) 1-14. | MR | Zbl

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. | Zbl

L.D. Berkovitz (1974) : Lower semi-continuity of integral functionals. Trans. Amer. Math. Soc. 192, 51-58. | MR | Zbl

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. | MR | Zbl

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. | Zbl

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.

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. | MR | Zbl

D.P. Bertsekas (1975) : Non differentiable optimization via approximation. Math. Progr. Study 3 1-25. | MR | Zbl

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.

R.L. Bishop (1969) : Manifolds of negative curvature. Trans. Amer. Math. Soc. 145 1-49. | MR | Zbl

F.S. De Blasi (1976) : On the differentiability of multifunctions. Pacific. J. Math. 66, 67-81. | MR | Zbl

L.M. Blumenthal (1953) : Theory and applications of distance geometry. The Clarendon Press, Oxford. | MR | Zbl

V.G. Boltyanskii (1975) : The method of tents in the theory of extremal problems Russian Math. Surveys. 30 (3) 1-54. | Zbl

J. Borwein (1977) : Weak local supportability and application to approximation (preprint) Dahlousie Univ. Halifax.

D.G. Bourgin (1973) : Fixed point and min-max theorems. Pacific J. Math. 45 (2) 403-412. | MR | Zbl

H. Brezis - L. Nirenberg - S. Stampacchia (1972) : A remark on Ky Fan's minimax principle. Bull. Un. Mat. Ital. 6 (4), 293-300. | MR | Zbl

F.E. Browder (1967) : A new generalization of the Schauder fixed point theorem. Math. Ann. 174 (1967) 285-290. | Zbl

F.E. Browder (1973) : Normal solvability for nonlinear mappings into Banach spaces Bull. Amer. Math. Soc. 79, 328-350.

R.F. Brown (1971) : The Lefschetz fixed point theorem. Scott, Foresman and C°, Glenview, Illinois. | MR | Zbl

Yu. D. Burago - V.A. Zalgaller (1977) : Convex sets in Riemannian spaces of non-negative curvature. Russian Math. Surveys 32 (3), 1-57. | Zbl

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. | Zbl

C. Castaing - M. Valadier (1977) : Convex analysis and measurable multifunctions. Lectures Notes in Math n° 580. Springer Verlag. New-York. | MR | Zbl

L. Cesari (1974) : An existence theorem without convexity conditions. SIAM J. Control 12 (2) 319-331. | MR | Zbl

D. Chenais (1975) : On the existence of a solution in a domain identification problem. J. Math. Analysis Appl. 52 (2) 189-219. | MR | Zbl

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. | MR | Zbl

Y. Cherruault (1970) : Minimization de fonctionnelles non convexes. Rend. Mat. VI série 3 (1971) 777-785, MR 44 # 7715. | Zbl

G. Chichilnisky (1977) : Nonlinear functional analysis and optimal economic growth J. Math. Anal. Appl. 61 (2) 504-520. | MR | Zbl

F.H. Clarke (1975) : Generalized gradients and applications. Trans. Amer. Math. Soc. 205, 247-262. | MR | Zbl

F.H. Clarke (1975) : The Euler-Lagrange Differential inclusion. J. Diff. Eq. 19, 80-90. | MR | Zbl

F.H. Clarke (1975) : Admissible relaxation in variational and control problems. J. Math. Anal. and Appl. 51, 557-576. | MR | Zbl

F.H. Clarke (1976) : Optimal solutions to differential inclusions. J. Optim. Th. Appl. 19 (3) 469-478. | MR | Zbl

F.H. Clarke (1976) : A new approach to Lagrange multipliers. Math. Operations Research 1, 165-174. | MR | Zbl

F.H. Clarke (1977) : Multiple integrals of Lipschitz functions in the calculus of variations. Proc. Amer. Math. Soc. 64 (2) 260-264. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

J.P. Crouzeix (1976) : Conjuguay in quasi-convex analysis. Proceedings conference Murat le Quaire. Lectures Notes in Economies and Math. Syst. n° 144. | Zbl

J.P. Crouzeix (1977) : Contribution à l'étude des fonctions quasiconvexes. Thèse, Univ. Clermont-Ferrand II. | MR

J.P. Crouzeix (1976) : Dualité quasi-convexe. Séminaire d'analyse numérique, Univ. de Clermont.

J.W. Daniel (1971) : The approximate minimization of functionals. Prentice Hall, Englewood Cliffs N.Y. | MR | Zbl

I.I. Daniljuk (1972) : On integral functionals with a variable domain of integration. Proc. Steklov Inst. Math. 118, Amer. Math. Soc. Providence (1976). | Zbl

L. Danzer, B. Grünbaum, V. Klee (1963) : Helly's theorem and its relatives. Proc. Symp. Pure Math. 7, 101-180. Amer. Math. Soc. Providence. | MR | Zbl

G. Dantzig - J. Folkman - N. Shapiro (1967) : On the continuity of the minimum set of continuous fonctions. Journ. Math. Anal. Appl. 17, 519-548. | MR | Zbl

A. Deleanu (1959) : Théorie des points fixes sur les rétractes de voisinage des espaces convexoïdes. Bull. Soc. Math. France 87, 235-243. | Numdam | MR | Zbl

E. Dierker (1974) : Topological methods in Walrasian economics. Lect. notes in Economics n° 92, Springer Verlag, Berlin. | MR | Zbl

J. Diestel - J.J. Uhl (1977) : Vector measures. Math. Survey n° 15, Amer. Math. Soc., Providence, Rhode Island. | MR | Zbl

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. | MR | Zbl

S. Dolecki, S. Kurcyusz (1976) : Convexité généralisée et optimisation. C.R. Acad. Sci. Paris 238, A 91-94. | MR | Zbl

S. Dolecki, S. Kurcyusz (1978) : On Φ-convexity in extremal problems. SIAM J. Control and Opt. 16 (2) 277-300. | MR | Zbl

S. Dubuc (1960) : Topological convex spaces. Ph. D. THESIS, Cornell Univ. N.Y.

M. Edelstein (1966) : Farthest points of sets in uniformly convex Banach spaces. J. London Math. Soc. 43, 375-377. | Zbl

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. | MR | Zbl

I. Ekeland (1974) : On the variational principle. J. Math. Anal. and Appl. 47 (2) ; 324-353. | MR | Zbl

I. Ekeland (1979) : Nonconvex minimization problems. Bull. Amer. Math. Soc. (new series) 1 (3) 443-474. | MR | Zbl

I. Ekeland - G. Lebourg (1975) : Sous gradients approchés et applications. C.R. Acad. Sc. Paris 281 A 219-222. | MR | Zbl

I. Ekeland - G. Lebourg (1976) : Generic Frechet differentiability and perturbed optimization problems in Banach spaces. Trans. Amer. Math. Soc. 224 (2) 193-216. | MR | Zbl

I. Ekeland - R. Temam (1974) : Analyse convexe et problèmes variationnels. Dunod-Gauthier-Villars, Paris. Edité en anglais par North Holland avec un appendice. | MR | Zbl

I. Ekeland - M. Valadier (1971) : Représentation of set-valued mappings. J. Math. Anal. Appl. 35, 621-629. | MR | Zbl

J.P. Evans - F.J. Gould (1970) : Stability in nonlinear programming. Operation Research 18, 107-118. | MR | Zbl

K. Fan (1953) : Minimax theorems. Proc. Nat. Acad. Sci. 39, 42-47. | MR | Zbl

A.V. Fiacco (1976) : Sensitivity analysis for nonlinear programming using penalty methods. Math. Program. 10 287-311. | MR | Zbl

F. Ficheux - G.S. Rubinstein (1975) : Préordres quasi-convexes (en russe) Optimizacija 16 (33), 127-146, Zentralblatt 46012 N 327. | MR | Zbl

A. F. Filippov (1967) : Classical solutions of differential equations with multivalued right hand side. SIAM J. Control 5, 609-621. | MR

A.F. Filippov (1971) : On the existence of solutions of multivalued differential equations. Math. Zametki 10, 307-313. | MR | Zbl

A.L. Fradkov (1976) : Duality theorems for certain non convex extremal problems Siberian Math J. 14 (2) ; 247-263. | Zbl

S. Gautier (1979) : Différentiabilité des multiapplications. Publications Math. de Pau.

J. Gauvin - J.W. Tolle (1977) : Differential stability in nonlinear programming. SIAM J. Control 15 (2), 294-311. | MR | Zbl

J.S. Gibson - I.G. Clark (1977) : Sensitivity analysis for a class of evolution equations. J. Math. Anal. Appl. 58 (1), 22-31. | MR | Zbl

C. Godet - Thobie (1975) : Multimesures et multimesures de transition. Thèse, Montpellier.

A.A. Goldstein (1977) : Optimization of Lipschitz continuous functions. Math. Programming 13 (1) 38-48. | MR | Zbl

G.S. Goodman - J. Hoffmann - Jørgensen (1969) : Support functions and the function space embedding of infinite dimensional convex sets. Core discussion Papers, Louvain.

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. | MR | Zbl

W.B. Gordon (1972) : Convex functions and harmonic maps. Proc. Amer. Math. Soc. 33 (2) 433-437. | MR | Zbl

W.B. Gordon (1974) : The existence of geodesics joining two given points. J. Diff. Geom. 9, 443-450. | MR | Zbl

M.J. Greenberg - W.P. Pierskalla (1975) : Stability theorems for infinitely constrained mathematical programs. J. Optim. Th. Appl. 16 (5/6) 409-428. | MR | Zbl

D. Gromoll (1970) : Manifolds of non negative curvature. Actes Congrès Intern. Math. t.2, 177-180. Nice. | MR | Zbl

R. Guesnerie (1969) : Optimum de Pareto et ensembles de production non convexes. Bull. Math. Economiques 2, 31-60.

J. Gwinner (1977) : Closed images of convex multivalued mappings in linear topological spaces with applications. J. Math. Anal. Appl. 60, 75-86. | MR | Zbl

H. Halkin (1976) : Mathematical programming without differentiability. In “Calculus of variations and control theory”, edited by D.L. Russel, Academic Press. | MR | Zbl

B. Halpern - G. Bergman (1968) : A fixed point theorem for inward and outward maps. Trans. Amer. Math. Soc. 130, 353-358. | MR | Zbl

B. Halpern (1970) : Fixed point theorems for set-valued maps in infinite dimensional spaces. Math. Ann. 189, 87-98. | MR | Zbl

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. | Zbl

H. Hermes (1969) : Existence and properties of solutions of xє R(t,x). SIAM, Study Applied Math 5, 188-193.

H. Hermes (1970) : The generalized differential equation xєR(t,x). Advances in Math. 4, 149-169. | MR | Zbl

W. Hildenbrand, D. Schmeidler, S. Zamir (1973) : Existence of approximate equilibria and cores Econometrica 41 (1973) 1159-1166. | Zbl

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. | Zbl

J.B. Hiriart-Urruty (1978) : Conditions nécessaires d'optimalité pour un programme stochastique avec recours. SIAM J. Control and Opt. 16 (2) 317-329. | MR | Zbl

Hoang Tuy (1974) : On an axiomatic for extremal problems and first order necessary conditions. Soviet Math. Dokl. 15 (3) 978-983. | Zbl

Hoang Tuy (1974) : On a general minimax principle. Soviet Math. Doklady 15 (6) 1689-1693. | Zbl

L. Hormander (1954) : Sur la fonction d'appui des ensembles convexes dans un espace localement convexe. Ark. Mat. 3, 181-186. MR 16-720. | MR | Zbl

R.E. Huff - P.D. Morris (1976) : Geometric characterization of the Radon-Nikodym property in Banach spaces. Studia Math. 56 (2) 157-164. | MR | Zbl

M. Hukuhara (1967) : Intégration des applications mesurables dont la valeur est un compact convexe. Funk. Ekvac. 10, 205-223. | MR | Zbl

F.N. Huggins (1977) ; Bounded slope variationand generalized convexity. Proc. AMS 65 (1), 65-69. | MR | Zbl

A.D. Ioffe (1977) : Sur la semi-continuité des fonctionnelles intégrales. C.R. Acad. Sc. Paris 284, 807-809. | MR | Zbl

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. | MR | Zbl

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.

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. | Zbl

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. | MR | Zbl

H. Kaczinski - C. Olech (1974) : Existence of solutions of orientor fields with nonconvex right hand side, Ann. Polon. Math. 29, 61-66. | Zbl

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. | MR | Zbl

W.A. Kirk (1976) : Caristi's fixed point theorem and metric convexity (preprint). | MR

V. Klee (1951) : Convex sets in linear spaces Duke Math. J. 18, 443-466. | MR | Zbl

H. Kneser (1952) : Convexe Raume, Archiv. der Math. 3, 198-206. | MR | Zbl

G. Knowles (1977) : Some remarks on infinite dimentional nonlinear control without convexity. SIAM J. contol and Optim. 15 (5), 830-840. | MR | Zbl

J.M. Lasry (1975) : Communication personnelle.

J.M. Lasry (1976) : Structure de l'ensemble des solutions d'une équation différentielle multivoque. Conséquences. Journées de contrôle, Metz, mai 76.

J.M. Lasry - R. Robert (1976) : Analyse non linéaire multivoque. Cahiers de Math. de la décision Univ. Paris IX. n° 7611. | Zbl

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. | MR | Zbl

G. Lebourg (1975) : Valeur moyenne pour gradient généralisé. C.R. Acad. Sc. Paris ; 281, 795-797. | MR | Zbl

G. Lebourg (1977) : Generic differentiability of Lipschitzian functions. Cahiers de Math. de la décision. Univ. Paris Dauphine, n° 7704.

J. Leray (1945) : Sur la forme des espaces topologiques et sur les points fixes des représentations. J. Math. Pures Appl. 24, 95-167. | Numdam | MR | Zbl

J. Leray (1959) : Théorie des points fixes, indice total et nombre de Lefschetz. Bull. Soc. Math. de France 87, 221-233. | Numdam | MR | Zbl

P. Levine, J.C. Pomerol (1976) : C-Closed mappings and Kuhn-Tucker vectors in convex programming. Core Discussion paper n° 7620. Louvain.

P. Levine, J.C. Pomerol (1978) : Quelques extensions des théorèmes "inf-sup", C.R. Acad. Sci. Paris 287, A 565-567. | MR | Zbl

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. | MR | Zbl

C. Lemarechal (1975) : Note on an extension of Davidon's method to non-differentiable functions. Math. Progr. Study 3, 110-126.

A. Lew (1975) : Stability, prediction-correction and dynamic programming. J. Optim. Th. and Appl. 17 (314), 229-238. | MR | Zbl

C. Lobry (1972) : Aspects qualitatifs de la théorie des équations différentielles multivoques. Séminaire Math. Appl. Bordeaux, exp. n°3, Publications Univ. Bordeaux 72-73.

D.G. Mahajan, M.N. Vartak (1977) : Generalization of some duality theorems in non-linear programming. Math. Programm. 12 (3) 392-405. | MR | Zbl

C. Malivert (1977) : Optimisation sur une variété anguleuse ou un fermé non convexe. Thèse 3ème cycle, Pau.

O.L. Mangasarian (1965) : Pseudo-convex functions. J. SIAM Control 3, 281-290. | MR | Zbl

O.L. Mangasarian (1969) : Nonlinear programming. Mc Graw Hill, New-York. | Zbl

O.L. Mangasarian (1975) : Second and higher order duality in nonlinear programming. J. Math. Anal. Appl. 51 (3), 557-576. | MR | Zbl

M. Martelli - A. Vignoli (1974) : On differentiability of multivalued maps. Bull. Un. Math. Ital. (4) 10, 701-702. | MR | Zbl

D.H. Martin (1975) : On the continuity of the maximum in parametric linear programming. J. Optim. Th. and Appl. 17 (3/4) 205-210. | MR | Zbl

R.H. Martin Jr (1976) : Nonlinear operators and differential equations in Banach spaces. Wiley-Interscience, New-York. | Zbl

A. Mas Colell (1979) : A selection theorem for open graph correspondances with starshaped valued. J. Math. Anal. Appl.68 (1), 273-275. | MR | Zbl

H. Massam - S. Zlobec (1974) : Various definitions of the derivative in mathematical programming, Math. Pro. 7 (2), 144-161. | MR | Zbl

E. Mazet (1974) : Problèmes relatifs aux applications harmoniques. Thèse, Paris.

K. Menger (1928) : Untersuchungen über allgemenie Metrik. Math. Annalen 100, 75-163. | JFM

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. | MR | Zbl

P. Michel (1973) : Problème des inégalités. Application à la programmation et au contrôle optimal. Bull. Soc. Math. de France 101, 413-439. | Numdam | MR | Zbl

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. | MR

S. Mitetelu (1976) : Kuhn-Tucker conditions for non-linear programming with quasi-convex constraints. Revue Roum. Math. Pures Appl. 21 (7) 903-909. | Zbl

J.J. Moreau (1963) : Fonctions à valeurs dans [-∞, +∞] ; notions algébriques, Faculté des Sciences de Montpellier, séminaires de Math. (multigraphié). | MR

C.B. Morrey (1966) : Multiple integrals in the calculus of variations. Springer-Verlag. New-York. | MR | Zbl

F. Murat - J. Simon (1974) : Quelques résultats sur le contrôle par un domaine géométrique. Laboratoire d'analyse numérique. Univ. Paris VI.

F. Murat - J. Simon (1976) : Sur le contrôle par un domaine géométrique. Laboratoire d'analyse numérique. Univ. Paris VI.

D. Netzer - U. Passy (1975) : A note on the maximum of quasi-concave functions. J. Optim. Th. Appl. 16 (5/6) 565-570. | MR | Zbl

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. | Zbl

C. Olech (1976) : Weak lower semi-continuity of integral functionals. J. Optim. Th. and Appl. 19 (1) 3-17. | MR | Zbl

C. Olech (1969) : Existence theorems for optimal control problems involving multiple integrals. J. Diff. Eq. 6, 512-526 MR 39 # 7488. | MR | Zbl

C. Olech (1975) : Existence of solutions of nonconvex orientor fields. Boll. Univ. Mat. Ital. 11 (4) fasc. 3 suppl. 189-197. | MR | Zbl

R. Pallu De La Barriere (1974) : Fonctions sous-linéarisables et principe de Pontryagin, Publications Math. Univ. de Bordeaux I (1973-1974) (3), 65-72.

B. Palmerio - A. Derviaux (1974): Identification de domaines et problèmes de frontière libre. Thèse 3ème cycle. Nice.

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. | MR | Zbl

T. Parthasarathy, T.E.S. Raghavan (1971) : Some topics in two-person games, Amer. Elsevier, New-York. | MR | Zbl

J.P. Penot (1974) : Sous-différentiels de fonctions numériques non convexes. C.R. Acad. Sc. Paris 278 A 1553-1555. | MR | Zbl

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. | Zbl

J.P. Penot (1978) : Utilisation des sous-différentiels généralisés en optimisation. 1er colloque AFCET - S.M.F. tome 3, 69-85. | Zbl

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.

D.W. Peterson (1974) : On sensitivity in optimal control problems. J. Optim. Th. and Appl. 13 (1), 56-73. | MR | Zbl

G. Pianigiani (1977) : On the fundamental theory of multivalued differential equations. J. Diff. Equat. 25 (I), 30-38. | MR | Zbl

A. Plis (1963) : Trajectories and quasi trajectories of an orientor field. Bull. Acad. Polon. Sci. Mat. Astronom. Phys. 11, 369-370. | MR | Zbl

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. | MR | Zbl

J. Ponstein (1967) : Seven kinds of convexity. SIAM Review 9 (1), 115-119. | MR | Zbl

B.N. Pshenichnyi (1971) : Necessary conditions for an extremum. Pure and Applied Math. Marcel Dekker, New-York. | MR | Zbl

T. Rader (1973) : Absolutely continuous constrained miximizers. J. Optim. Th. and Appl. 12 (2), 107-128. | MR | Zbl

H. Radstrom (1952) : An embedding theorem for spaces of convex sets. Proc. Amer. Math. Soc. 3, 165-169. | MR | Zbl

C. Raffin (1970) : Sur les programmes convexes définis dans des espaces vectoriels topologiques. Annales Inst. Fourier 20 (1), 457-491. | Numdam | MR | Zbl

S. Reich (1977) : Approximate selections, best approximations, fixed points and invariant sets (preprint).

A.W. Roberts-D.E. Varberg (1973) : Convex functions. Academic Press, New-York. | MR | Zbl

A.W. Roberts-D.E. Varberg (1973) : Functions of bounded convexity, Bull. Amer. Math. Soc. 75, 568-572. | MR | Zbl

S.M. Robinson (1975) : A characterization of stability in linear programming. MRC Techn. Report n° 1542, Univ. of Wisconsin. Madison.

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. | MR | Zbl

R.T. Rockafellar (1970) : Convex analysis. Princeton Math. Series Princeton, Univ. Press. Princeton, New-York. | MR | Zbl

R.T. Rockafellar (1974) : Augmented Lagrange multiplier functions and duality in non-convex programming. SIAM J. Control. 12 (2), 268-285. | MR | Zbl

R.T. Rockafellar (1975) : Existence theorems for general control problems of Bolza and Lagrange. Advances in Math. 15, 312-315. | MR | Zbl

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.

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. | MR | Zbl

G.S. Rubinstein (1973): Caractérisation d'une classe de fonctions convexes. Optimizacija 9 (26), 165-180. | MR | Zbl

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. | MR | Zbl

S. Schaible (1977) : Second order characterization of pseudo-convex quadratic function. J. Optim. Th. Appl. 21 (1) 15-26. | MR | Zbl

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. | MR | Zbl

E.J. Mc. Shane (1967) : Relaxed controls and variational problems. SIAM J. Control 5, 438-485. | MR | Zbl

E. Silverman (1973) : A necessary condition in the calculus of variations. Proc. Amer. Math. Soc. 37 462-464 MR 47 # 7555. | MR | Zbl

E. Silverman (1973) : Strong quasi-convexity. Pacific J. Math. 46 549-554 MR 48 # 9488. | MR | Zbl

A.D. Solomon (1975) : On parameter dependance of the solution to an extremal problem. J. Optim. Th. and Appl. 17 (1/2), 163-168. | MR | Zbl

J. Stoer, C. Witzgall (1970) : Convexity and optimization in finite dimensions I., Springer Verlag, Berlin. | MR | Zbl

M.H. Stone (1949) : Postulates for the barycentric calculus. Annali. di. Mat. (4) 29, 25-30, MR 12, 45. | MR | Zbl

S. Szufla (1973) : Solutions sets of nonlinear equations. Bull. Acad. Pol. Sc. 21 (11) 971-976. | MR | Zbl

S. Szufla (1977) : On the structure of solution sets of differential and integral equations in Banach Spaces. Annales Polon. Math. 34, 165-177. | MR | Zbl

S. Tagawa (1974) : Generalized convexities of continuous functions and their application to mathematical programming. Bull. Math. Stat. 16 (1/2), 115-121. | MR | Zbl

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. | MR | Zbl

L. Thibault (1976) : Propriétés des sous-différentiels de fonctions localement lipschitziennes définies sur un espace de Banach séparable. Applications. Thèse 3ème cycle. Montpellier. | MR

L. Thibault : Subdifferentials of Compactly Lipschitzian Vector-Valued Functions (to appear in Ann. Mat. Pura Appl.). | Zbl

L. Thibault : Mathematical Programming and Optimal Control Problems Defined by Compactly Lipschitzian Mappings (to appear).

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.

J.F. Toland (1977) : On the stability of rotating heavy chains idem n° 82.

J.F. Toland (1978) : Duality in nonconvex optimization. idem N° 78 et J. Math. Anal. Appl. 66 (2), 399-414. | MR | Zbl

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. | MR | Zbl

G. Vidossich (1971) : On the structure of the set of solutions of nonlinear equations. J. Math. Anal. Appl. 34, 502-617. | MR | Zbl

J. Warga (1962) : Relaxed variational problems. J. Math. Anal. Appl. 4, 111-128. | MR | Zbl

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.

Ja. I. Zabotin (1973) : Conditions for the extremum of a functional in the presence of constraints. Kibernetika (Kiev) (6), 65-70 MR 50 # 1723. | MR | Zbl

V. Zirler (1973) : On some extremal problems in Banach spaces. Math. Scand. 32, 214-224. | MR | Zbl

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. | MR | Zbl

J.P. Zolesio (1979) : Identification de domaines par déformations. Thèse, Nice.

Cité par Sources :