Variational characterization of the contingent epiderivative

DOI10.1016/j.jmaa.2007.01.110zbMath1135.49011OpenAlexW2070934575MaRDI QIDQ2642193

Miguel Sama, Luis Rodríguez-Marín

Publication date: 20 August 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.01.110

zbMATH Keywords

set-valued mapsvariational characterizationcontingent epiderivativeordered space

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonsmooth analysis (49J52)

Related Items (25)

Higher-order efficiency conditions for constrained vector equilibrium problems ⋮ The role of directional compactness in the existence and computation of contingent epiderivatives ⋮ Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints ⋮ Optimality Conditions for Vector Equilibrium Problems in Terms of Contingent Epiderivatives ⋮ New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces ⋮ Duality results for interval-valued pseudoconvex optimization problem with equilibrium constraints with applications ⋮ Necessary optimality conditions for second-order local strict efficiency for constrained nonsmooth vector equilibrium problems ⋮ Optimality and duality for nonsmooth mathematical programming problems with equilibrium constraints ⋮ Weak and strong subgradients of set-valued maps ⋮ Scalar Lagrange multiplier rules for set-valued problems in infinite-dimensional spaces ⋮ The existence of contingent epiderivative for a set-valued mapping and vector variational-like inequalities ⋮ Some remarks on the existence and computation of contingent epiderivatives ⋮ \(\tau ^w\)-contingent epiderivatives in reflexive spaces ⋮ Epidifferentiability of the map of infima in Hilbert spaces ⋮ Scalar multiplier rules in set-valued optimization ⋮ Stability analysis of conically perturbed linearly constrained least-squares problems by optimizing the regularized trajectories ⋮ Scalarization and optimality conditions for strict minimizers in multiobjective optimization via contingent epiderivatives ⋮ Optimality conditions in terms of contingent epiderivatives for strict local Pareto minima in vector optimization problems with constraints ⋮ Epidifferentiability and hypodifferentiability of pseudoconvex maps in set-optimization problems ⋮ Computation formulas and multiplier rules for graphical derivatives in separable Banach spaces ⋮ Necessary and sufficient optimality conditions for constrained vector equilibrium problems using contingent hypoderivatives ⋮ OPTIMALITY OF GLOBAL PROPER EFFICIENCY FOR CONE-ARCWISE CONNECTED SET-VALUED OPTIMIZATION USING CONTINGENT EPIDERIVATIVE ⋮ On sufficiency and duality theorems for nonsmooth semi-infinite mathematical programming problem with equilibrium constraints ⋮ Some non-smooth optimality results for optimization problems with vanishing constraints via Dini-Hadamard derivative ⋮ Approximate solutions for nonconvex set-valued optimization and vector variational inequality

Cites Work

• About contingent epiderivatives
• Existence theorems in vector optimization
• Optimality conditions for set-valued optimization problems
• Contingent epiderivatives and set-valued optimization
• Variational methods in partially ordered spaces
• The existence of contingent epiderivatives for set-valued maps
• An Introduction to Banach Space Theory
• Set-valued analysis

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