Saddle-point criteria in an eta-approximation method for nonlinear mathematical programming problems involving invex functions

摘要

In this paper, the eta-approximation method introduced by Antczak (Ref. 1) for solving a nonlinear constrained mathematical programming problem involving invex functions with respect to the same function eta is extended. In this method, a so-called eta-approximated optimization problem associated with the original mathematical programming problems is constructed; moreover, an eta-saddle point and an eta-Lagrange function are defined. By the help of the constructed eta-approximated optimization problem, saddle-point criteria are obtained for the original mathematical programming problem. The equivalence between an eta-saddle point of the eta-Lagrangian of the associated eta-approximated optimization problem and an optimal solution in the original mathematical programming problem is established.