Semi E-convex Multi-Objective Programming Problems

Abstract

In this thesis, we interested in optimizing multi-objective programming problems which are involving generalized semi E-convex functions. The study goes through three broad lines. The first concerns with thegeneralized semi E-convex functions which are quasi semi E-convex functions and pseudo semi E-convex functions. Optimality criteria for nonlinear programming problem involving those functions are investigated. Along the second line, the characterization of efficientsolutions for multi-objective programming problems involving semi E-convex functions are considered. We are interested in characterizing those problems by weighting and ε-constraint approaches. The necessary and sufficient conditions for a feasible solution to be an efficient or properly efficient solution are derived. An approximation algorithm for finding efficient solutions for semi E-convex multi-objective programming problems is investigated along the Third line.