Sequential approximate optimality conditions for a constrained convex vector minimization problem and application to multiobjective fractional programming problem - A. Ed-dahdah; M. Laghdir; M. Echchaabaoui; M. Mabrouk (Iranian Journal of Numerical Analysis and Optimization)
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.