Some algorithms for classes of split feasibility problems involving paramonotone equilibria and convex optimization

Abstract

In this paper, we first introduce a new algorithm which involves projecting each iteration to solve a split feasibility problem with paramonotone equilibria and using unconstrained convex optimization. The strong convergence of the proposed algorithm is presented. Second, we also revisit this split feasibility problem and replace the unconstrained convex optimization by a constrained convex optimization. We introduce some algorithms for two different types of objective function of the constrained convex optimization and prove some strong convergence results of the proposed algorithms. Third, we apply our algorithms for finding an equilibrium point with minimal environmental cost for a model in electricity production. Finally, we give some numerical results to illustrate the effectiveness and advantages of the proposed algorithms.

New Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem

“…The operator T = P C (I − λ∇f ) is well known to be nonexpansive (see [14,30] and the references therein). Several authors have have considered different iterative algorithm for constrained convex minimization problems (see [4,9,13,19,34] and the references therein). We now give our main results Theorem 8.2.…”

Inexact simultaneous projection method for solving bilevel equilibrium problems

“…In recent years, it is attractive by many researchers. There are increasing interests in studying solution methods for this problem such as the hybrid steepest descent methods of Yamada [33] where S i (i ∈ I) are nonexpansive mappings, subgradienttype method of Iiduka [20] and other [34,15,14].…”