On gap functions for nonsmooth multiobjective optimization problems
type: Item
instance of: scholarly article
title: On gap functions for nonsmooth multiobjective optimization problems
zbMATH Open document ID: 1405.90115
author: Giuseppe Caristi
author: Nader Kanzi
author: Majid Soleimani-Damaneh
published in: Optimization Letters
publication date: 2018-04-19T00:00:00Z
review text: It is known that, if at some feasible solution of a differentiable multiobjective problem the set-valued gap function introduced by \textit{G. Y. Chen} et al. [Eur. J. Oper. Res. 111, No. 1, 142--151 (1998; Zbl 0944.90079)] contains zero, then that solution is efficient. In the present work, the authors prove that the converse statement is true if the solution is proper, and give a nonsmooth version of gap functions for convex problems. They also introduce a single-valued gap function and show that a feasible solution of a quasiconvex problem is efficient if and only if the gap function takes the value zero at that solution, provided that the so-called nonvanishing constraint qualification (NCQ) is satisfied. Note that the condition (NCQ) is not applicable to unconstrained single-criterion problems.
reviewed by: Dinh The Luc
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 6861696
zbMATH Keywords: multiobjective optimization
zbMATH Keywords: nonsmooth optimization
zbMATH Keywords: gap function
zbMATH Keywords: Clarke's subgradient
MaRDI profile type: Publication
full work available at URL: s11590-017-1110-4
OpenAlex ID: W2584483637
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DOI: 10.1007/S11590-017-1110-4
description: scientific article; zbMATH DE number 6861696