SADDLE POINTS CRITERIA VIA A SECOND ORDER 77-APPROXIMATION APPROACH FOR NONLINEAR MATHEMATICAL PROGRAMMING INVOLVING SECOND ORDER INVEX FUNCTIONS

摘要

In this paper, by using the second order η-approximation method introduced by Antczak [3], new saddle point results are obtained for a nonlinear mathematical programming problem involving second order invex functions with respect to the same function η. Moreover, a second order η-saddle point and a second order η-Lagrange function are defined for the so-called second order η-approximated optimization problem constructed in this method. Then, the equivalence between an optimal solution in the original mathematical programming problem and a second order η-saddle point of the second order 77-Lagrangian in the associated second order η-approximated optimization problem is established. Finally, some example of using this approach to characterize of solvability of some O.R. problem is given.