strict Fejér monotonicity – Optimization Online

A necessary condition for the guarantee of the superiorization method

Published: 2025/02/06

Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization bounded perturbations resilience, dynamic string-averaging, feasibility-seeking, guarantee question of superiorization, strict Fejér monotonicity, superiorization

We study a method that involves principally convex feasibility-seeking and makes secondary efforts of objective function value reduction. This is the well-known superiorization method (SM), where the iterates of an asymptotically convergent iterative feasibility-seeking algorithm are perturbed by objective function nonascent steps. We investigate the question under what conditions a sequence generated by an SM … Read more

Strict Fejér Monotonicity by Superiorization of Feasibility-Seeking Projection Methods

Published: 2014/05/28

Yair Censor

Alexander J. Zaslavski

Constrained Nonlinear Optimization, Parallel Algorithms bounded perturbation resilience, constrained minimization, convex feasibility problem, dynamic string-averaging projections, strict Fejér monotonicity, subgradients, superiorization methodology, superiorized version of an algorithm

We consider the superiorization methodology, which can be thought of as lying between feasibility-seeking and constrained minimization. It is not quite trying to solve the full fledged constrained minimization problem; rather, the task is to find a feasible point which is superior (with respect to the objective function value) to one returned by a feasibility-seeking … Read more