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Saddle-Point Criteria in an η-Approximation Method for Nonlinear Mathematical Programming Problems Involving Invex Functions

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  • T. Antczak

    (University of Łódź)

Abstract

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

Suggested Citation

  • T. Antczak, 2007. "Saddle-Point Criteria in an η-Approximation Method for Nonlinear Mathematical Programming Problems Involving Invex Functions," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 71-87, January.
    • Handle: RePEc:spr:joptap:v:132:y:2007:i:1:d:10.1007_s10957-006-9069-9
    DOI: 10.1007/s10957-006-9069-9
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    References listed on IDEAS

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    1. X.Q. Yang, 2003. "On the Gap Functions of Prevariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 437-452, February.
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