Document Type : Research Paper

Authors

• Nader Kanzi ¹
• Fahimeh-alsadat Kazemi Bafruei ²

¹ Department of Mathematics, Payame Noor University (PNU), Tehran, Iran

² Department of Mathematics. Payame noor University.

Abstract

In this paper, we introduce two novel dual formulations for optimization problems governed by inequality constraints. The considered problems are characterized by differentiable functions. The proposed dual problems are parameterized by a set-valued parameter, where different values of this parameter reduce the dual formulations to the Wolfe and Mond–Weir dual problems. Consequently, the proposed dual problem serves as a unified generalization of both. Furthermore, we establish the weak, strong, converse, restricted converse, and strict converse duality results for the formulated dual problems.

Keywords

• ِDual problem
• Duality results
• Constraint qualification
• Optimality