An η-Approximation Approach for Nonlinear Mathematical Programming Problems Involving Invex Functions

Abstract

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

Key Words:

• η-Approximated optimization problem
• Invex function with respect to η
• Optimality
• Duality

Mathematics Subject Classification:

• Primary 90C26
• 90C30
• 90C46
• Secondary 26B25