Special Class of Second-Order Non-Differentiable Symmetric Duality Problems with (G,αf)-Pseudobonvexity Assumptions

Ramu Dubey,Lakshmi Narayan Mishra,Rifaqat Ali

doi:10.3390/math7080763

Abstract

In this paper, we introduce the various types of generalized invexities, i.e., α f -invex/ α f -pseudoinvex and ( G , α f ) -bonvex/ ( G , α f ) -pseudobonvex functions. Furthermore, we construct nontrivial numerical examples of ( G , α f ) -bonvexity/ ( G , α f ) -pseudobonvexity, which is neither α f -bonvex/ α f -pseudobonvex nor α f -invex/ α f -pseudoinvex with the same η . Further, we formulate a pair of second-order non-differentiable symmetric dual models and prove the duality relations under α f -invex/ α f -pseudoinvex and ( G , α f ) -bonvex/ ( G , α f ) -pseudobonvex assumptions. Finally, we construct a nontrivial numerical example justifying the weak duality result presented in the paper.

Highlights

Decision making is an integral and indispensable part of life
The benefit of second-order duality is considered over first-order as it gives all the more closer limits
Expanding the idea of [3] by Jayswal [4], a new kind of problem has been defined and duality results demonstrated under generalized convexity presumptions over cone requirements

Summary

Introduction

Decision making is an integral and indispensable part of life. Every day, one has to make decisions of some type or the other. Expanding the idea of [3] by Jayswal [4], a new kind of problem has been defined and duality results demonstrated under generalized convexity presumptions over cone requirements. Jayswal et al [5] defined higher order duality for multiobjective problems and set up duality relations utilizing higher order ( F, α, ρd)-V-Type I suspicions. Suneja et al [6] utilized the idea of ( F, α, σ )-type I capacities to build up K-K-T-type sufficient optimality conditions for the non-smooth multiobjective fractional programming problem. Under the assumption of G-invexity, Antczak [11] introduced the concept of the G-invex function and derived some optimality conditions for the constrained problem. We build different nontrivial examples, which legitimize the definitions, as well as the weak duality hypothesis introduced in the paper

Preliminaries and Definitions

Conclusions