On some nonsmooth equilibrium constrained minimization models using epiderivative

¹ Department of Mathematics, School of Advanced Engineering, UPES, Dehradun 248007, India
² Department of Mathematics, Graphic Era (Deemed to be University), Dehradun 248002, India
³ Department of Applied Mathematics, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania
⁴ Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
⁵ Fundamental Sciences Applied in Engineering Research Center (SFAI), National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania

^* Corresponding author: savin.treanta@upb.ro

Received: 28 October 2024
Accepted: 13 May 2025

Abstract

In this article, we explore duality problems of Wolfe and Mond-Weir type, tailored for mathematical programming problems that encompass non-smooth functions and equilibrium constraints, denoted by the abbreviation NSMPEC. This investigation is grounded in the realm of real Banach spaces. We will begin by presenting, conditions that serve as a sufficient basis for achieving optimality within the (NSMPEC) framework. Specifically, these conditions require the objective and constraint functions to exhibit higher-order strong invexity at the specific point under consideration. We also extend our research to formulate and prove the weak and strong duality theorems in the sense of the original problem and its dual. However, the assumptions required for this theorem assume some conditions on the higher-order strong invexity of the objective and constraint functions. To demonstrate the practical importance of the established results, we present a number of practical examples.