A new step size selection strategy for the superiorization methodology using subgradient vectors and its application for solving convex constrained optimization problems

Abstract

Abstract This paper presents a novel approach for solving convex constrained minimization problems by introducing a special subclass of quasi-nonexpansive operators and combining them with the superiorization methodology that utilizes subgradient vectors. Superiorization methodology tries to reduce a target function while seeking a feasible point for the given constraints. We begin by introducing a new class of operators, which includes many well-known operators used for solving convex feasibility problems. Next, we demonstrate how the superiorization methodology can be combined with the introduced class of operators to obtain superiorized operators. To achieve this, we present a new formula for the step size of the perturbations in the superiorized operators. Finally, we propose an iterative method that utilizes the superiorized operators to solve convex constrained minimization problems. We provide examples of image reconstruction from projections (tomography) to demonstrate the capabilities of our proposed iterative method.