A class of generalized invex functions and vector variational-like inequalities

Ru Li,Guolin Yu

doi:10.1186/s13660-017-1345-8

Ru Li, Guolin Yu

Open Access

https://doi.org/10.1186/s13660-017-1345-8

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Abstract

In this paper, a class of generalized invex functions, called (alpha,rho,eta)-invex functions, is introduced, and some examples are presented to illustrate their existence. Then we consider the relationships of solutions between two types of vector variational-like inequalities and multi-objective programming problem. Finally, the existence results for the discussed variational-like inequalities are proposed by using the KKM-Fan theorem.

Highlights

As we all know, convexity and generalized convexity of functions play an important role in the field of optimization theory and its application
We are about to introduce the following Stampacchia and Minty vector variationallike inequalities, respectively, with their weak formulations, which will be used to ensure the efficient solutions of the problem (MP)
We end this paper by presenting the following existence theorem for Minty vector variational-like inequality (MVVI)

Summary

Introduction

Convexity and generalized convexity of functions play an important role in the field of optimization theory and its application. In Section , the relationships between Stampacchia and Minty invex vector variational-like inequalities and (α, ρ, η)-invex multi-objective programming problem are discussed. Section gives the existence theorems of solution of Stampacchia and Minty vector variational-like inequality under the hypothesis of (α, ρ, η)-monotonicity.

Results

Conclusion