An η-approximation approach for nonlinear mathematical programming problems involving invex functions

A new approach to a solution of a nonlinear constrained mathematical programming problem and its Mond-Weir duals is introduced. An eta-approximated problem associated with a primal nonlinear programming problem is presented that involves eta-approximated functions constituting the primal problem. The equivalence between the original mathematical programming problem and its associated eta-approximated optimization problem is established under invexity assumption. Furthermore, eta-approximated dual problems in the sense of Mond-Weir are introduced for the obtained eta-approximated optimization problem in this method. By the help of eta-approximated dual problems some duality results are established for the original mathematical programming problem and its original duals.