Algorithmic Approach to the Split Problems

Ming Ma

doi:10.1155/2013/218964

Abstract

This paper deals with design algorithms for the split variational inequality and equilibrium problems. Strong convergence theorems are demonstrated.

Highlights

Problem 1 can be applied to many practical problems such as signal processing and image reconstruction
We can find the prototype of Problem 1 in intensity-modulated radiation therapy; see, for example, [1,2,3]
Our main purpose is to study the following split problem involved in the variational inequality and equilibrium problems

Summary

Introduction

We can find the prototype of Problem 1 in intensity-modulated radiation therapy; see, for example, [1,2,3] Based on this relation, many mathematicians were devoted to study the split feasibility problem and develop its iterative algorithms. Our main purpose is to study the following split problem involved in the variational inequality and equilibrium problems. We are devoted to study (4) with operator Ψ being a nonlinear mapping For this purpose, we develop an iterative algorithm for solving the split problem (4). Let C be a nonempty closed convex subset of a real Hilbert space H. Assume t(lih0ma, 1ts)ua, pna+nn1→d≤∞{δδ(nn1}≤−is0γa(no)sarenq∑u+∞ ne=nδ1cn|eδγnnsγ,antw|ish

Main Results

It follows that

Using hence