Theorems of the alternative and optimization with set-valued maps

DOI10.1023/A:1026407517917zbMath0966.90071OpenAlexW167154149MaRDI QIDQ1841577

Xiao Qi Yang, Yang, Xinmin, Guang-Ya Chen

Publication date: 18 February 2001

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1026407517917

zbMATH Keywords

vector optimization set-valued maps generalized convexity optimality conditions equivalent conditions theorem of the alternatives

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Multi-objective and goal programming (90C29) Nonlinear programming (90C30)

Related Items (36)

Approximate weakly efficient solutions of set-valued vector equilibrium problems ⋮ A study of interval optimization problems ⋮ Image convexity of generalized systems with infinite-dimensional image and applications ⋮ A note on ``Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality ⋮ An alternative theorem for set-valued maps via set relations and its application to robustness of feasible sets ⋮ Generalized Higher-Order Optimality Conditions for Set-Valued Optimization under Henig Efficiency ⋮ Error bounds for generalized mixed vector equilibrium problems via a minimax strategy ⋮ Generalized Motzkin theorems of the alternative and vector optimization problems ⋮ Nearly subconvexlike set-valued maps and vector optimization problems ⋮ The semi-\(E\) cone convex set-valued map and its applications ⋮ Scalarization of set-valued optimization problems with generalized cone subconvexlikeness in real ordered linear spaces ⋮ Optimality conditions of generalized subconvexlike set-valued optimization problems based on the quasi-relative interior ⋮ Second-order optimality conditions for cone-subarcwise connected set-valued optimization problems ⋮ KKT conditions for weak\(^\ast\) compact convex sets, theorems of the alternative, and optimality conditions ⋮ Unnamed Item ⋮ \(\epsilon\)-optimality conditions of vector optimization problems with set-valued maps based on the algebraic interior in real linear spaces ⋮ Weak sharp minima for piecewise linear multiobjective optimization in normed spaces ⋮ Hartley proper efficiency in multifunction optimization ⋮ Moreau-Rockafellar theorems for nonconvex set-valued maps ⋮ The effects of adding objectives to an optimisation problem on the solution set ⋮ New second-order tangent epiderivatives and applications to set-valued optimization ⋮ Optimality conditions of set-valued optimization problem involving relative algebraic interior in ordered linear spaces ⋮ Optimality conditions of vector set-valued optimization problem involving relative interior ⋮ A generalized alternative theorem of partial and generalized cone subconvexlike set-valued maps and its applications in linear spaces ⋮ Calmness and exact penalization in constrained scalar set-valued optimization ⋮ The relationship between ic-cone-convexness and nearly cone-subconvexlikeness ⋮ New generalized convexity notion for set-valued maps and application to vector optimization ⋮ Optimality conditions for strictly efficient solutions in set-valued optimization ⋮ Characterizations of Benson proper efficiency of set-valued optimization in real linear spaces ⋮ Second-Order M-Composed Tangent Derivative and Its Applications ⋮ An optimal alternative theorem and applications to mathematical programming ⋮ Scalarizations and Lagrange multipliers for approximate solutions in the vector optimization problems with set-valued maps ⋮ Approximate proper efficiency in vector optimization ⋮ Lagrangian multipliers for generalized affine and generalized convex vector optimization problems of set-valued maps ⋮ Approximate Benson efficient solutions for set-valued equilibrium problems ⋮ E-Benson proper efficiency in vector optimization

Cites Work

This page was built for publication: Theorems of the alternative and optimization with set-valued maps