Proper approximate solutions and \(\varepsilon\)-subdifferentials in vector optimization: basic properties and limit behaviour

DOI10.1016/j.na.2012.11.016zbMath1285.90058OpenAlexW2043023177MaRDI QIDQ1934989

Bienvenido Jiménez, Vicente Novo Sanjurjo, César Gutiérrez, Lidia Huerga

Publication date: 30 January 2013

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.2012.11.016

zbMATH Keywords

vector optimization \(\varepsilon\)-subdifferential linear scalarization proper \(\varepsilon\)-efficiency proper \(\varepsilon\)-subdifferential nearly subconvexlikeness

Mathematics Subject Classification ID

Convex programming (90C25) Multi-objective and goal programming (90C29) Nonsmooth analysis (49J52) Programming in abstract spaces (90C48) Optimality conditions for problems in abstract spaces (49K27)

Related Items (13)

Sequential \(\varepsilon\)-subdifferential calculus for scalar and vector mappings ⋮ Optimality conditions for approximate proper solutions in multiobjective optimization with polyhedral cones ⋮ Chain rules for a proper \(\varepsilon\)-subdifferential of vector mappings ⋮ Variants of the Ekeland variational principle for approximate proper solutions of vector equilibrium problems ⋮ Approximation of Weak Efficient Solutions in Vector Optimization ⋮ Duality related to approximate proper solutions of vector optimization problems ⋮ Unnamed Item ⋮ Formulae for the conjugate and the subdifferential of the supremum function ⋮ Optimality Conditions for Weakly ϵ-Efficient Solutions of Vector Optimization Problems with Applications ⋮ A unified concept of approximate and quasi efficient solutions and associated subdifferentials in multiobjective optimization ⋮ Approximate solutions of vector optimization problems via improvement sets in real linear spaces ⋮ Ekeland variational principles involving set perturbations in vector equilibrium problems ⋮ Limit Behavior of Approximate Proper Solutions in Vector Optimization

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