The approximate subdifferential of composite functions

DOI10.1017/S0004972700015276zbMath0785.58010MaRDI QIDQ3137358

Lionel Thibault, Abderrahim Jourani

Publication date: 1 November 1993

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

subdifferentiallocally Lipschitzianstrongly compactly Lipschitzian

Mathematics Subject Classification ID

Programming in abstract spaces (90C48) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20)

Related Items (19)

Constraint qualifications and Lagrange multipliers in nondifferentiable programming problems ⋮ A Fritz John optimality condition using the approximate subdifferential ⋮ Qualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problems ⋮ Topological properties of the approximate subdifferential ⋮ Lagrangian conditions for vector optimization in Banach spaces ⋮ First order approximations to nonsmooth mappings with application to metric regularity ⋮ Necessary optimality conditions and exact penalization for non-Lipschitz nonlinear programs ⋮ On a class of compactly epi-Lipschitzian sets ⋮ Metric regularity for strongly compactly Lipschitzian mappings ⋮ Relaxed constant positive linear dependence constraint qualification and its application to bilevel programs ⋮ DIRECTIONAL COMPACTNESS, SCALARIZATION AND NONSMOOTH SEMI-FREDHOLM MAPPINGS ⋮ Lagrange multipliers for multiobjective programs with a general preference ⋮ Verifiable Conditions for Openness and Regularity of Multivalued Mappings in Banach Spaces ⋮ Lagrange Multiplier Rules for Weakly Minimal Solutions of Compact-Valued Set Optimization Problems ⋮ Unnamed Item ⋮ Optimality conditions for vector equilibrium problems with constraint in Banach spaces ⋮ Existence of Lagrange multipliers for set optimization with application to vector equilibrium problems ⋮ Coderivatives of multivalued mappings, locally compact cones and metric regularity ⋮ Extensions of Fréchet \(\varepsilon\)-subdifferential calculus and applications

Cites Work

• Stability and regular points of inequality systems
• Approximate Subdifferentials and Applications. I: The Finite Dimensional Theory
• On Subdifferentials of Optimal Value Functions
• Extensions of subgradient calculus with applications to optimization
• The use of metric graphical regularity in approximate subdifferential calculus rules in finite dimensions

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