Nondifferentiable Multiobjective Programming Problem under Strongly K-Gf-Pseudoinvexity Assumptions

Ramu Dubey,Luis Manuel Sánchez Ruiz,Lakshmi Narayan Mishra,Deepak Umrao Sarwe

doi:10.3390/math8050738

Abstract

In this paper we consider the introduction of the concept of (strongly) K- G f -pseudoinvex functions which enable to study a pair of nondifferentiable K-G- Mond-Weir type symmetric multiobjective programming model under such assumptions.

Highlights

Duality mathematical programming is used in Economics, Control Theory, Business and other diverse fields
In the present paper we consider a pair of K-G-Mond-Weir type multiobjective symmetric dual program for which we establish the weak duality theorem, as well as the corresponding strong, and converse ones under K-G f -pseudo-invexity/strongly K-G f -pseudo-invexity assumptions
By using the notion of K-G f - pseudo-invex/ strongly K − G f - pseudo-invex functions we have established duality results for (KGMPP) /(KGNMPP)-Mond–Weir dual models applied in multiobjective nondifferentiable symmetric programming problems with objective cone and cone constraints, too

Summary

Introduction

Duality mathematical programming is used in Economics, Control Theory, Business and other diverse fields. Several definitions such as nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudoinvex functions have been introduced by Xianjun [7] By introducing these new concepts, sufficient optimality conditions for a nonsmooth multiobjective problem were obtained and, a fortiori, weak and strong duality results were established for a Mond-Weir type multiobjective dual program. In the present paper we consider a pair of K-G-Mond-Weir type multiobjective symmetric dual program for which we establish the weak duality theorem, as well as the corresponding strong, and converse ones under K-G f -pseudo-invexity/strongly K-G f -pseudo-invexity assumptions. In the process we construct a lemma that enables us to prove the strength and converse duality theorems under K-G f -pseudo-invexity/strongly K-G f -pseudo-invexity assumptions

Preliminaries and Definitions

K-G-Mond-Weir Type Primal Dual Model

K-N-G-Mond–Weir Type Nondifferentiable Dual Model

Conclusions