Yair Censor – Optimization Online

A new theorem of alternatives leading to sufficient conditions for the superiorization guarantee question of Dynamic String-Averaging in the inconsistent case

Published: 2026/07/29

We study the Superiorization Methodology (SM) in the context of the General Dynamic String-Averaging (GDSA) method in the inconsistent case (that is, where the input operators don’t have a common fixed point) which primarily aims at achieving convex feasibility while simultaneously reducing an objective function. In many scientific and real-world problems modeled as constrained minimization … Read more

On the boundedness of infinite products of relaxed projections: perturbations resilience and dynamic string-averaging

Published: 2026/07/29

Basic Sciences Applications, Convex Optimization, Infinite Dimensional Optimization Affine subspace, boundedness, control, dynamic string-averaging, half-space, infinite product, innately regular, perturbation resilience, relaxed projection, strongly nonexpansive mapping

Very recently (2026), Bauschke and Tung extended from finite- to infinite-dimensional Hilbert spaces a result published by Meshulam in 1996 (following an earlier result of Aharoni-Duchet-Wajnryb from 1984) regarding the boundedness of infinite products of relaxed projections onto a finite family of closed affine subspaces. In the present note we extend in various ways the … Read more

GPU-accelerated superiorization on constrained physical problems with SupPy

Published: 2026/07/03

Applications - OR and Management Sciences, Biomedical Applications, Constrained Nonlinear Optimization CT Image reconstruction, feasibility-seeking, Python SupPy, radiotherapy treatment planning, Seismic image reconstruction, superiorization method

The superiorization method (SM) is situated between feasibility-seeking and constrained optimization. Instead of aiming at the minimum of a given objective function over a constraint set, it seeks a feasible point at which the objective function value is reduced — though not necessarily minimal — compared to that reached by the feasibility-seeking algorithm alone. This … Read more

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

Published: 2026/03/16

Constrained Nonlinear Optimization, Convex Optimization Approximately shrinking operator, bounded perturbation resilience, bounded regularity, common fixed point problem, convex feasibility problem, dynamic string-averaging, Fej{\'e}r monotonicity, nonexpansive operators, strongly quasi-nonexpansive operators, superiorization

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

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 and Perturbation Resilience of Algorithms: A Continuously Updated Bibliography

Published: 2025/04/15, Updated: 2025/04/18

Yair Censor

Applications - Science and Engineering, Constrained Nonlinear Optimization constrained optimization, feasibility problem, perturbation resilience, superiorization methodology

This document presents a (mostly) chronologically-ordered bibliography of scientific publications on the superiorization methodology and perturbation resilience of algorithms which is compiled and continuously updated by us at: http://math.haifa.ac.il/yair/bib-superiorization-censor.html. Since the beginnings of this topic we try to trace the work that has been published about it since its inception. To the best of our … Read more

An iterative process for the feasibility-seeking problem with sets that are unions of convex sets

Published: 2025/04/08

Constrained Nonlinear Optimization, Convex Optimization feasibility-seeking, floorplanning, non-convex sets, projections onto sets expandable in convex sets., unions of convex sets

In this paper we deal with the feasibility-seeking problem for unions of convex sets (UCS) sets and propose an iterative process for its solution. Renewed interest in this problem stems from the fact that it was recently discovered to serve as a modeling approach in fields of applications and from the ongoing recent research efforts … Read more

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

New results related to cutters and to an extrapolated block-iterative method for finding a common fixed point of a collection of them

Published: 2024/10/30, Updated: 2025/09/04

Convex Optimization, Nonlinear Optimization, Parallel Algorithms block-iterative algorithm, common fixed point, cutter, extrapolation, weight function

Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous applications in science and engineering. We consider an extrapolated block-iterative method with dynamic … Read more

Immunity to Increasing Condition Numbers of Linear Superiorization versus Linear Programming

Published: 2024/08/07

Basic Sciences Applications, Constrained Nonlinear Optimization, Linear Programming bounded perturbations, condition number, feasibility-seeking, Gurobi., ill--posed problem, linear programming, linear superiorization, Scipy

Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at finding a point that fulfills the constraints and has the minimal value of the objective function … Read more