bounded perturbation resilience – Optimization Online

Strong convergence, perturbation resilience and superiorization of Generalized Modular String-Averaging with infinitely many input operators

Published: 2026/03/16

We study the strong convergence and bounded perturbation resilience of iterative algorithms based on the Generalized Modular String-Averaging (GMSA) procedure for infinite sequences of input operators under a general admissible control. These methods address a variety of feasibility-seeking problems in real Hilbert spaces, including the common fixed point problem and the convex feasibility problem. In … Read more

General Perturbation Resilient Dynamic String-Averaging for Inconsistent Problems with Superiorization

Published: 2025/07/02

Kay Barshad

Yair Censor

Constrained Nonlinear Optimization, Convex Optimization Approximately shrinking operator, bounded perturbation resilience, bounded regularity, coherence, coherent sequence of operators, common fixed point problem, convex feasibility problem, dynamic string-averaging, Fej{\'e}r monotonicity, metric projection, nonexpansive operator, strong coherence, strongly coherent sequence of operators, superiorization, weak convergence, weak regularity.

In this paper we introduce a General Dynamic String-Averaging (GDSA) iterative scheme and investigate its convergence properties in the inconsistent case, that is, when the input operators don’t have a common fixed point. The Dynamic String-Averaging Projection (DSAP) algorithm itself was introduced in an 2013 paper, where its strong convergence and bounded perturbation resilience were … Read more

Superiorization: The asymmetric roles of feasibility-seeking and objective function reduction

Published: 2022/12/30

Yair Censor

Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization basic algorithm, bounded perturbation resilience, constraints modeling, derivative-free, dynamic string-averaging projections, feasibility-seeking, guarantee problem, proximity function, proximity-target curve., superiorization, superiorized algorithm

The superiorization methodology can be thought of as lying conceptually between feasibility-seeking and constrained minimization. It is not trying to solve the full-fledged constrained minimization problem composed from the modeling constraints and the chosen objective function. Rather, the task is to find a feasible point which is “superior” (in a well-defined manner) with respect to … Read more

The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

Published: 2022/07/13

Francisco J. Aragón Artacho

Yair Censor

Aviv Gibali

David Torregrosa-Belén

Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization basic algorithm, bounded perturbation resilience, intensity-modulated radiation therapy (IMRT), restart, split minimization problem, subvectors, superiorization

In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced … Read more

Can linear superiorization be useful for linear optimization problems?

Published: 2016/10/06

Yair Censor

Constrained Nonlinear Optimization, Linear Programming, Problem Solving Environments agmon-motzkin-schoenberg algorithm, algorithmic operator, bounded perturbation resilience, feasibility-seeking, linear feasibility problem, linear inequalities, linear programming, linear superiorization, simplex algorithm, superiorization

Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point whose linear … 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

Feasibility-Seeking and Superiorization Algorithms Applied to Inverse Treatment Planning in Radiation Therapy

Published: 2014/02/04

Biomedical Applications, Convex Optimization bounded perturbation resilience, feasibility-seeking, inverse planning problem in radiation therapy, projection methods, superiorization

We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the intensity vector over a large system of linear two-sided inequalities. The SM can be viewed conceptually as lying between feasibility-seeking … Read more