Approximate subdifferential and metric regularity: The finite-dimensional case

DOI10.1007/BF01580860zbMath0714.49023OpenAlexW2072344559MaRDI QIDQ750873

Abderrahim Jourani, Lionel Thibault

Publication date: 1990

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01580860

zbMATH Keywords

finite- dimensional multifunctionsgraphical metric regularitypartial approximate subdifferentialspseudo-Lipschitz multifunctions

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Set-valued functions (26E25) Set-valued maps in general topology (54C60)

Related Items (36)

Metric regularity of the feasible set mapping in semi-infinite optimization ⋮ Metric regularity and second-order necessary optimality conditions for minimization problems under inclusion constraints ⋮ Qualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problems ⋮ Metric regularity and subdifferential calculus in Banach spaces ⋮ On regularity and stability in semi-infinite optimization ⋮ Stable local minimizers in semi-infinite optimization: Regularity and second-order conditions ⋮ Topological properties of the approximate subdifferential ⋮ Equi-surjective systems of linear operators and applications ⋮ Metric Regularity and Optimality Conditions in Nonsmooth Optimization ⋮ Inverse and implicit function theorems for nonsmooth maps in Banach spaces ⋮ A generalized karush-kuhn-tucki optimality condition without constraint qualification using tl approximate subdifferential ⋮ Regularity and strong sufficient optimality conditions in differentiable optimization problems ⋮ First order approximations to nonsmooth mappings with application to metric regularity ⋮ Topological characterization of the approximate subdifferential in the finite-dimensional case ⋮ On metric regularity of multifunctions ⋮ Metric regularity for strongly compactly Lipschitzian mappings ⋮ On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems ⋮ Metric projection and compatibly parameterized families of prox-regular sets in Hilbert space ⋮ Compactly epi-lipschitzian sets and a-subdifferentials in wt-spaces ⋮ An implicit-function theorem for \(C^{0,1}\)-equations and parametric \(C^{1,1}\)-optimization ⋮ A chain rule for first- and second-order epiderivatives and hypoderivatives ⋮ Newton's method for fully parameterized generalized equations ⋮ Complete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of Multifunctions ⋮ Metric regularity of the sum of multifunctions and applications ⋮ A chain rule for parabolic second-order epiderivatives ⋮ Enhanced metric regularity and Lipschitzian properties of variational systems ⋮ Verifiable Conditions for Openness and Regularity of Multivalued Mappings in Banach Spaces ⋮ Metric regularity of composition set-valued mappings: metric setting and coderivative conditions ⋮ Metric regularity, tangent sets, and second-order optimality conditions ⋮ Regularity of implicit solution mapping to parametric generalized equation ⋮ On metric regularity in metric spaces ⋮ Constrained nonsmooth problems of the calculus of variations ⋮ Error bounds for eigenvalue and semidefinite matrix inequality systems ⋮ Locally compactly Lipschitzian mappings in infinite dimensional programming ⋮ Epiderivatives of the marginal function in nonsmooth parametric optimization ⋮ Higher–Order Necessary Optimality Conditions for a Nonsmooth Extremum Problem

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