SADDLE POINTS CRITERIA VIA A SECOND ORDER eta-APPROXIMATION APPROACH FOR NONLINEAR MATHEMATICAL PROGRAMMING INVOLVING SECOND ORDER INVEX FUNCTIONS
In this paper, by using the second order eta-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 eta. Moreover, a second order eta-saddle point and a second order eta-Lagrange function are defined for the so-called second order eta-approximated optimization problem constructed in this method. Then, the equivalence between an optimal solution in the original mathematical programming problem and a second order eta-saddle point of the second order eta-Lagrangian in the associated second order eta-approximated optimization problem is established. Finally, some example of using this approach to characterize of solvability of sonic O.R. problem is given.
second order eta-saddle point second order eta-lagrange function second order eta-approximated optimization problem second order invex function with respect to eta second order optimality conditions