A condition for the stability of ideal efficient solutions in parametric\n vector optimization via set-valued inclusions

2021/10/31 by Amos Uderzo, Uderzo, Amos
Computer Science · Mathematics · Engineering · #Optimization and Variational Analysis #Advanced Optimization Algorithms Research #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2111.00461

Abstract

In present paper, an analysis of the stability behaviour of ideal efficient\nsolutions to parametric vector optimization problems is conducted. A sufficient\ncondition for the existence of ideal efficient solutions to locally perturbed\nproblems and their nearness to a given reference value is provided by refining\nrecent results on the stability theory of parameterized set-valued inclusions.\nMore precisely, the Lipschitz lower semicontinuity property of the solution\nmapping is established, with an estimate of the related modulus. A notable\nconsequence of this fact is the calmness behaviour of the ideal value mapping\nassociated to the parametric class of vector optimization problems. Within such\nan analysis, a refinement of a recent existence result specific for ideal\nefficient solutions to unperturbed problem is also discussed.\n

Related

• On the quantitative solution stability of parameterized set-valued inclusions
• On some global implicit function theorems for set-valued inclusions with applications to parametric vector optimization
• Marginal Analysis of Convex Optimization Problems with Set-Valued Inclusion Constraints
• R-regularity of set-valued mappings under the relaxed constant positive\n linear dependence constraint qualification with applications to parametric\n and bilevel optimization
• Sensitivity Analysis in Parametric Convex Vector Optimization