On the set of weakly efficient minimizers for convex multiobjective programming (original) (raw)
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The study of the multiobjective programming problems is one of the great significance in optimization theory (see [1]). A certain situation is when the objective function is a nondiferentiable vector function. To treat this case we consider a constrained multiobjective programming problem. The class of invex functions was introduced by Hanson (see [2]). This class of functions is designed to relax the assumptions of the convexity which are imposed on functions when we want to state the sufficient optimality conditions. In the specialized literature exists some concepts concerning the class of invex functions (see [3], [4]). One of these approaches is that proposed by H. Slimani and M.S. Radjef (see [4]). In their study the invexity for a differentiable vector function is solved by searching the invexity for each component. On the other hand, for studying the invexity of a nondifferentiable vector function with respect to the same function η exist an other approach (see [5], [6],) wh...