On G-invexity-type nonlinear programming problems

² Department of Statistics and Operational Research, Faculty of SSCC and Communication, University of C´adiz Av. de la Universidad, 11406-Jerez, Spain

IJOCTA 2016, 5(1), 13–20; https://doi.org/10.11121/ijocta.01.2015.00202

Submitted: 28 April 2014 | Published: 16 January 2015

© 2015 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )

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Abstract

In this paper, we introduce the concepts of KT-G-invexity and W D-G-invexity for the considered differentiable optimization problem with inequality constraints. Using KT-G-invexity notion, we prove new necessary and sufficient optimality conditions for a new class of such nonconvex differentiable optimization problems. Further, the so-called G-Wolfe dual problem is defined for the considered extremum problem with inequality constraints. Under W D-G-invexity assumption, the necessary and sufficient conditions for weak duality between the primal optimization problem and its G-Wolfe dual problem are also established.

Keywords

Mathematical programming;W D-G-invexity;G-Karush-Kuhn-Tucker point;G-Wolfe dual problem

Conflict of interest

The authors declare they have no competing interests.

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