Algorithms for approximating minimization problems in Hilbert spaces

摘要

In this paper, we study the following minimization problem minx∈Fix(S)∩Ωμ2〈Bx,x〉+12‖x‖2−h(x), where B is a bounded linear operator, μ≥0 is some constant, h is a potential function for γ̄f, Fix(T) is the set of fixed points of nonexpansive mapping S and Ω is the solution set of an equilibrium problem. This paper introduces two new algorithms (one implicit and one explicit) that can be used to find the solution of the above minimization problem.