×

zbMATH — the first resource for mathematics

On generalized differentials and subdifferentials of Lipschitz vector- valued functions. (English) Zbl 0492.46036

MSC:
46G05 Derivatives of functions in infinite-dimensional spaces
58C06 Set-valued and function-space-valued mappings on manifolds
90C48 Programming in abstract spaces
26B05 Continuity and differentiation questions
90C30 Nonlinear programming
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Castaing, C.; Valadier, M., Convex analysis and measurable multifunctions, () · Zbl 0346.46038
[2] Clarke, F.H., Generalized gradients and applications, Trans. am. math. soc., 205, 247-262, (1975) · Zbl 0307.26012
[3] Clarke, F.H., A new approach to Lagrange multipliers, Math. operations res., 2, 165-174, (1976) · Zbl 0404.90100
[4] Clarke, F.H., On the inverse function theorem, Pacific J. math., 64, 97-102, (1976) · Zbl 0331.26013
[5] \scChristensen J. P. R., Topology and Borel structure, Math. Studies 10, Notas Mathematica.
[6] Christensen, J.P.R., On sets of Haar measure zero in abelian Polish groups, Israël J. math., 13, 255-260, (1972)
[7] Fabian, M., Concerning interior mapping theorem, Comment math. univ. carolinae, 20, 345-356, (1979) · Zbl 0393.46008
[8] Halkin, H., Interior mapping theorem with set-valued derivative, J. analyse math., 30, 200-207, (1976) · Zbl 0349.49016
[9] \scHiriart-Urruty J. B., Characterizations of the plenary hull of the generalized Jacobian matrix. Math. Progress Study, to appear. · Zbl 0532.26007
[10] Hiriart-Urruty, J.B., New concepts in nondifferentiable programming, Bull. soc. math. fr., 60, 57-85, (1979) · Zbl 0469.90071
[11] Hiriart-Urruty, J.B.; Thibault, L., Existence et caractérisation de différentielles généralisées d’applications localement lipschitziennes d’un Banach séparable dans un Banach réflexif séparable, C.r. hebd. Séanc. acad. sci. Paris, 290, 1091-1094, (1980) · Zbl 0441.46035
[12] Ioffe, A.D., Différentielles généralisées d’applications localement lipschitziennes d’un espace de Banach dans un autre, C.r. hebd. Séanc. acad. sci. Paris, 289, 637-640, (1979) · Zbl 0421.46039
[13] Ioffe, A.D., Nonsmooth analysis: differential calculus of nondifferentiable mappings, Trans. am. math. soc., 266, 1-56, (1981) · Zbl 0651.58007
[14] Lebourg, G., Valeur moyenne pour gradient généralisé, C.r. hebd. Séanc. acad. sci. Paris, 281, 795-797, (1975) · Zbl 0317.46034
[15] Pourciau, B.H., Analysis and optimization of Lipschitz continuous mappings, J. optimization theory applic., 22, 311-351, (1977) · Zbl 0336.26008
[16] Robinson, S.M., Regularity and stability for convex multivalued functions, Math. op. res., 1, 130-145, (1976) · Zbl 0418.52005
[17] \scRockafellar R. T., Directional Lipschitzian functions and subdifferential calculus, Proc. Lond. math. Soc., 331-355. · Zbl 0413.49015
[18] Rubinov, A.M., Sublinear operators and operator-convex sets, Siberian math. J., 17, 289-296, (1976) · Zbl 0354.46016
[19] Rubinov, A.M., Sublinear operators and their applications, Russ. math. surv., 32, 115-175, (1977) · Zbl 0384.47002
[20] Sweetser, T.H., A minimal set-valued strong derivative for vector-valued Lipschitz functions, J. optimization theory applic., 23, 549-562, (1977) · Zbl 0345.26005
[21] Sweetser, T.H., A set-valued strong derivative in infinite dimensional spaces, with applications in Hilbert spaces, () · Zbl 0345.26005
[22] Thibault, L., Quelques propriétés des sous-différentiels de fonctions localement lipschitziennes définies sur un espace de Banach séparable, Sem. d’analyse convexe, (1975), exposé no. 16, Montpellier · Zbl 0357.46049
[23] Thibault, L., Subdifferentials of compactly Lipschitzian vector-valued functions, Ann. math. pura appl., 125, 157-192, (1980) · Zbl 0486.46037
[24] Thibault, L., Sur LES fonctions compactement lipschitziennes et leurs applications: programmation mathématique, contrôle optimal, espérance conditionnelle, ()
[25] Thibault, L., Subdifferentials of nonconvex vector-valued functions, J. math. anal. applic., 86, 319-344, (1982) · Zbl 0492.58005
[26] \scThibault L., On evolution problems associated with moving convex sets, J. Aust. math. Soc., to appear.
[27] Warga, J., Derivative containers, inverse functions and controllability, (), 13-46
[28] Yamamuro, S., Differential calculus in topological linear spaces, () · Zbl 0336.58006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.