Regularized gradient-projection methods for equilibrium and constrained convex minimization problems

Ming Tian,Li-Hua Huang

doi:10.1186/1029-242x-2013-243

Abstract

In this article, based on Marino and Xu's method, an iterative method which combines the regularized gradient-projection algorithm (RGPA) and the averaged mappings approach is proposed for finding a common solution of equilibrium and constrained convex minimization problems. Under suitable conditions, it is proved that the sequences generated by implicit and explicit schemes converge strongly. The results of this paper extend and improve some existing results. MSC: 58E35; 47H09; 65J15

Highlights

Let H be a real Hilbert space with the inner product ·, · and the induced norm ·
T is nonexpansive if Tx – Ty ≤ x – y for all x, y ∈ H
In this paper, motivated and inspired by the above results, we introduce a new iterative method: x ∈ H and

Summary

Introduction

Let H be a real Hilbert space with the inner product ·, · and the induced norm ·. They proved the sequence {xn} converges strongly to a point q ∈ U ∩ EP(φ), which solves the variational inequality (A – γ V )q, q – z ≤ , z ∈ U ∩ EP(φ).

Results

Conclusion