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Characterization of Clarke’s tangent and normal cones in finite and infinite dimensions. (English) Zbl 0515.49013

MSC:
49K27 Optimality conditions for problems in abstract spaces
46G05 Derivatives of functions in infinite-dimensional spaces
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
49J45 Methods involving semicontinuity and convergence; relaxation
49M37 Numerical methods based on nonlinear programming
46B20 Geometry and structure of normed linear spaces
90C30 Nonlinear programming
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References:
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[2] Aubin, J.P.; Clarke, F.H., Shadow prices and duality for a class of optimal control problems, SIAM J. control optim., 17, 567-586, (1979) · Zbl 0439.49018
[3] Bishop E. & Phelps R.R., The support functionals of a convex set in convexity (Edited by V.L. Klee), Proc. Symp. Pure Math. 7, 27-35. · Zbl 0149.08601
[4] Clarke, F.H., Generalized gradients and applications, Trans. am. math. soc., 205, 247-262, (1975) · Zbl 0307.26012
[5] Clarke, F.H., Generalized gradients of Lipschitz functionals, Adv. math., 40, 52-67, (1981) · Zbl 0463.49017
[6] Clarke, F.H., The erdmann condition and Hamiltonian inclusions in optimal control and the calculus of variations, Can. J. math., 32, 494-507, (1980) · Zbl 0461.49007
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[9] Hiriart-Urruty, J.B., Tangent cones, generalized gradients and mathematical programming in Banach spaces, Math. opl. res., 4, 79-97, (1979) · Zbl 0409.90086
[10] Penot, J.P., A characterization of tangential regularity, Nonlinear analysis, 5, 625-643, (1981) · Zbl 0472.58010
[11] Rockafellar, R.T., Clarke’s tangent cones and the boundaries of closed sets in \(R\)^n, Nonlinear analysis, 3, 145-154, (1979) · Zbl 0443.26010
[12] Rockafellar, R.T., Generalized directional derivatives and subgradients of nonconvex functions, Can. J. math., 32, 257-280, (1980) · Zbl 0447.49009
[13] Rockafellar, R.T., Proximal subgradients, marginal values, and augmented Lagrangians in nonconvex optimization, Math. opl. res., 6, 424-436, (1981) · Zbl 0492.90073
[14] Rockafellar, R.T., La theorie des sous-gradients et ses applications à l’optimisation, (1978), Les Presses de l’Université de Montréal
[15] Rockafellar, R.T., The theory of subgradients and its applications to problems of optimization, (1981), Heldermann Berlin · Zbl 0462.90052
[16] Thibault, L., Quelques propriétés des sous-différentials de fonctions réelles localement lipschitziennes definies sur un espace de Banach séparable, C.R. hebd. Séanc. acad. sci. Paris, ser A-B, 282, A507-A510, (1976)
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