Stability Results for Ekeland's ε-Variational Principle and Cone Extremal Solutions

DOI10.1287/moor.18.1.173zbMath0779.49015OpenAlexW2110829390MaRDI QIDQ4697090

Hedy Attouch, Hassan Riahi

Publication date: 29 June 1993

Published in: Mathematics of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1287/moor.18.1.173

zbMATH Keywords

set convergenceproper lower semicontinuous function

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items (45)

A note on lower semicontinuity of minimal points ⋮ Stability of the geometric Ekeland variational principle: Convex case ⋮ Convergence of the efficient sets ⋮ Stability of set-valued optimization problems with naturally quasi-functions ⋮ Nuclear and full nuclear cones in product spaces: Pareto efficiency and an Ekeland type variational principle ⋮ On epi-convergence for set-valued maps ⋮ Variational convergence for vector-valued functions and its applications to convex multiobjective optimization ⋮ Convergence Results for Henig Proper Efficient Solution Sets of Vector Optimization Problems ⋮ Cutting and scanning methods in set-valued analysis. I: An epigraphical and graphical calculus ⋮ Painlevé-Kuratowski stability of approximate efficient solutions for perturbed semi-infinite vector optimization problems ⋮ Convergence of the solution sets for set optimization problems ⋮ A Brézis-Browder principle on partially ordered spaces and related ordering theorems ⋮ Stability and scalarization of weak efficient, efficient and Henig proper efficient sets using generalized quasiconvexities ⋮ Stability for properly quasiconvex vector optimization problem ⋮ Further results on quasi efficient solutions in multiobjective optimization ⋮ On generalized Ekeland's variational principle and equivalent formulations for set-valued mappings ⋮ Stability results for convex vector-valued optimization problems ⋮ External and internal stability in set optimization ⋮ A unified concept of approximate and quasi efficient solutions and associated subdifferentials in multiobjective optimization ⋮ Some new results on stability of Ekeland's \(\varepsilon\)-variational principle ⋮ On the set of weakly efficient minimizers for convex multiobjective programming ⋮ Painlevé-Kuratowski stability of the solution sets to perturbed vector generalized systems ⋮ Approximate minima via the ekeland variational principle¹ ⋮ Efficiency and the uniform linear minorization of convex functions ⋮ Generalized \(\varepsilon \)-quasi-solutions in multiobjective optimization problems: existence results and optimality conditions ⋮ Ekeland's principle and nuclear cones: a geometrical aspect ⋮ Stability for convex vector optimization problems ⋮ Some variants of the Ekeland variational principle for a set-valued map ⋮ New concept of the ABB theorem ⋮ New stability results for Ekeland's \(\varepsilon\) variational principles for vector-valued and set-valued maps ⋮ Existence and Convergence of Optimal Points with Respect to Improvement Sets ⋮ Continuity of the efficient solution mapping for vector optimization problems ⋮ Convergence for vector optimization problems with variable ordering structure ⋮ Pareto optimizing and scalarly stationary sequences ⋮ Convergence of minimal and approximate minimal elements of sets in partially ordered vector spaces ⋮ Existence theorems of set optimization with set-valued maps ⋮ On Higher-Order Sensitivity Analysis of Parametric Henig Set-Valued Equilibrium Problems ⋮ Stability and scalarization for a unified vector optimization problem ⋮ Comparison of existence results for efficient points ⋮ On sensitivity in linear multiobjective programming ⋮ Stability results for properly quasi convex vector optimization problems ⋮ Painlevé-Kuratowski convergences of the solution sets for vector optimization problems with free disposal sets ⋮ Lower convergence of minimal sets in star-shaped vector optimization problems ⋮ Approximate efficiency and scalar stationarity in unbounded nonsmooth convex vector optimization problems ⋮ Generalized \({\varepsilon }\)-quasi solutions of set optimization problems

This page was built for publication: Stability Results for Ekeland's ε-Variational Principle and Cone Extremal Solutions