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

Document Type : Research Article

Authors

A. Ed-dahdah

M. Laghdir

M. Echchaabaoui

M. Mabrouk

Department of Mathematics, Faculty of Sciences, University of Chouaib Doukkali, El jadida, Morocco.

10.22067/ijnao.2025.90229.1534

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.

Keywords

Vector optimization

Approximate Pareto subdifferential of con-vex mappings

Sequential approximate optimality conditions

Subjects

• Optimization

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