Sequential approximate optimality conditions for a constrained convex vector minimization problem and application to multiobjective fractional programming problem

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Ed dahdah Ahmed; Laghdir Mohamed; Echchaabaoui El Mahjoub; Mabrouk M.

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION Year:2025 | Volume:15 | Issue:2 Page(s): 676-703

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Title

Sequential approximate optimality conditions for a constrained convex vector minimization problem and application to multiobjective fractional programming problem

Author(s)

Ed dahdah Ahmed | Laghdir Mohamed | Echchaabaoui El Mahjoub | Mabrouk M. | Issue Writer Certificate

Keywords

Vector optimization

Approximate Pareto subdifferential of con-vex mappings

Sequential approximate optimality conditions

Abstract

The aim of this paper is to establish sequential necessary and sufficient approximate optimality conditions for a constrained convex vector mini-mization problem without any constraint qualifications, characterizing the approximate proper and weak efficient solutions. The constraints are de-scribed by mappings taking values in different preorder vector spaces. Our approach is based essentially on the sequential approximate subdifferential calculus rule for the sums of a finite family of cone convex mappings. To illustrate our main result, an application to multiobjective fractional pro-gramming problem is given. Finally, we present an important subclass of such problems showing the applicability of the obtained conditions.

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