Minty Variational Principle for Nonsmooth Interval-Valued Vector Optimization Problems on Hadamard Manifolds

Savin Treanţă,Balendu Bhooshan Upadhyay,Priyanka Mishra

doi:10.3390/math10030523

Savin Treanţă, Balendu Bhooshan Upadhyay + Show 1 more

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https://doi.org/10.3390/math10030523

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Abstract

This article deals with the classes of approximate Minty- and Stampacchia-type vector variational inequalities on Hadamard manifolds and a class of nonsmooth interval-valued vector optimization problems. By using the Clarke subdifferentials, we define a new class of functions on Hadamard manifolds, namely, the geodesic LU-approximately convex functions. Under geodesic LU-approximate convexity hypothesis, we derive the relationship between the solutions of these approximate vector variational inequalities and nonsmooth interval-valued vector optimization problems. This paper extends and generalizes some existing results in the literature.

Highlights

Chen and Fang [28] established the relationship between Minty and Stampacchia vector variational inequalities and nonsmooth vector optimization problems under pseudoconvexity assumptions
Upadhyay and Mishra [29] studied the equivalence among approximate vector variational inequalities and interval-valued vector optimization problems involving approximate LU-pseudoconvex functions
The characterization and applications of approximate efficient solutions of vector optimization problems have been studied by several authors

Summary

Introduction

Many researchers studied vector variational inequalities and their generalizations arduously as an efficient tool to find optimal solutions of vector optimization problems Chen and Fang [28] established the relationship between Minty and Stampacchia vector variational inequalities and nonsmooth vector optimization problems under pseudoconvexity assumptions. Upadhyay and Mishra [29] studied the equivalence among approximate vector variational inequalities and interval-valued vector optimization problems involving approximate LU-pseudoconvex functions. The characterization and applications of approximate efficient solutions of vector optimization problems have been studied by several authors

Definition and Preliminaries p

Conclusions