New iterative methods for equilibrium and constrained convex minimization problems

Abstract

The gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. In this paper, we combine the GPA and averaged mapping approach to propose implicit and explicit composite iterative schemes for finding a common solution of an equilibrium problem and a constrained convex minimization problem. Then, we prove some strong convergence theorems which improve and extend some recent results.

A new iterative method for generalized equilibrium and constrained convex minimization problems

“…The equilibrium problem (1.1) includes, as special cases, numerous problems in physics, optimization and economics. Some authors (see [8,10,11,12,14,18]) have proposed useful methods for solving the equilibrium problem (1.1). Below we describe some of them.…”

A modified Halpern algorithm for approximating a common solution of split equality convex minimization problem and fixed point problem in uniformly convex Banach spaces

“…We denote the solution set of the Problem (4.1) by . Finding the common solutions of convex minimization problem, equilibrium problem and fixed point problem (4.1) has been studied recently by many authors in the setting of real Hilbert spaces (see for instance Abass et al 2018;Jolaoso et al 2018;Ogbuisi and Mewomo 2017;Okeke and Mewomo 2017;Tian and Liu 2012;Yazdi 2019). However, there are very few results on the split equality convex minimization problem and split equality equilibrium problems in higher Banach spaces.…”