Convergence analysis of an iterative algorithm for the extended regularized nonconvex variational inequalities

Ying Zhao,Rudong Chen,Luoyi Shi

doi:10.1186/s13660-017-1347-6

Ying Zhao, Rudong Chen + Show 1 more

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https://doi.org/10.1186/s13660-017-1347-6

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Abstract

In this paper, we suggest and analyze a new system of extended regularized nonconvex variational inequalities and prove the equivalence between the aforesaid system and a fixed point problem. We introduce a new perturbed projection iterative algorithm with mixed errors to find the solution of the system of extended regularized nonconvex variational inequalities. Furthermore, under moderate assumptions, we research the convergence analysis of the suggested iterative algorithm.

Highlights

1 Introduction Variational inequality was introduced and studied by Stampacchia [ ] in. It has been recognized as a suitable mathematical model to deal with many problems arising in different fields, such as optimization theory, game theory, partial differential equations, and economic equilibrium mechanics; see [ – ] and the references therein
Most of the results related to the existence of solutions and iterative methods for variational inequality problems have been investigated and considered so far to the case where the underlying set is convex
Inspired and motivated by the above works, in this paper, we introduce a new system of extended regularized nonconvex variational inequalities (SERNVI) and prove the equivalence between the SERNVI and a fixed point problem

Summary

Introduction

Variational inequality was introduced and studied by Stampacchia [ ] in. It has been recognized as a suitable mathematical model to deal with many problems arising in different fields, such as optimization theory, game theory, partial differential equations, and economic equilibrium mechanics; see [ – ] and the references therein. Most of the results related to the existence of solutions and iterative methods for variational inequality problems have been investigated and considered so far to the case where the underlying set is convex. They were introduced by Poliquin et al [ ] but called the uniformly prox-regular sets.

Results

Conclusion