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

T. Antczak ()
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T. Antczak: University of Łódź

Journal of Optimization Theory and Applications, 2007, vol. 132, issue 1, No 5, 87 pages

Abstract: 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.

Keywords: η-approximated optimization problem; η-saddle point; η-Lagrange function; invex function with respect to η; optimality (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10957-006-9069-9

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