Optimality conditions for set-valued maps with set optimization

DOI10.1016/j.na.2008.04.027zbMath1396.49009OpenAlexW1979268751MaRDI QIDQ1009616

J. Martínez

Publication date: 2 April 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.04.027

zbMATH Keywords

contingent derivativedirectional derivativeset-valued optimizationset optimization

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53)

Related Items (21)

On the stability of the solution set mappings to parametric set optimization problems ⋮ On the solution continuity of parametric set optimization problems ⋮ Necessary and sufficient conditions for set-valued maps with set optimization ⋮ Strict approximate solutions in set-valued optimization with applications to the approximate Ekeland variational principle ⋮ Approximate weak minimal solutions of set-valued optimization problems ⋮ Applications of Fell Topology to Closed Set-Valued Optimizations in Partially Ordered First Countable Topological Vector Spaces ⋮ Approximate solutions in set-valued optimization problems with applications to maximal monotone operators ⋮ On approximate solutions in set-valued optimization problems ⋮ Solving set optimization problems based on the concept of null set ⋮ Continuity of the solution set mappings to a parametric set optimization problem ⋮ Second-order optimality conditions for set optimization using coradiant sets ⋮ Optimality conditions in set optimization employing higher-order radial derivatives ⋮ Optimality for set-valued optimization in the sense of vector and set criteria ⋮ New order relations in set optimization ⋮ Lagrange Multiplier Rules for Weakly Minimal Solutions of Compact-Valued Set Optimization Problems ⋮ A new nonlinear scalarization function and applications ⋮ Continuity of solutions for parametric set optimization problems via scalarization methods ⋮ A Survey of Set Optimization Problems with Set Solutions ⋮ Unnamed Item ⋮ On Lagrange Multiplier Rules for Set-Valued Optimization Problems in the Sense of Set Criterion ⋮ Continuity of solutions mappings of parametric set optimization problems

Cites Work

• Scalarization and nonlinear scalar duality for vector optimization with preferences that are not necessarily a pre-order relation
• Nonconvex scalarization in set optimization with set-valued maps
• Differentiable selections and Castaing representations of multifunctions
• Directional derivatives for set-valued mappings and applications
• Contingent epiderivatives and set-valued optimization
• Some variants of the Ekeland variational principle for a set-valued map
• Approximations of nondifferentiable functions and local topological equivalence.
• On set-valued optimization.
• Set-relations and optimality conditions in set-valued maps
• Contingent derivatives of set-valued maps and applications to vector optimization
• Approximate Jacobian Matrices for Nonsmooth Continuous Maps and C¹-Optimization
• On cone convexity of set-valued maps
• Existence theorems of set optimization with set-valued maps
• The Lagrange Multiplier Rule in Set-Valued Optimization
• Set-valued analysis

This page was built for publication: Optimality conditions for set-valued maps with set optimization