<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We review the superiorization methodology, which can be thought of, in some cases, as lying between feasibility-seeking and constrained minimization. It is not quite trying to solve the full edged constrained minimization problem; rather, the task is to find a feasible point which is superior (with respect to an objective function value) to one returned by a feasibility-seeking only algorithm. We distinguish between two research directions in the superiorization methodology that nourish from the same general principle: Weak superiorization and strong superiorization and clarify their nature.</p></abstract>

We review the superiorization methodology, which can be thought of, in some cases, as lying between feasibility-seeking and constrained minimization. It is not quite trying to solve the full edged constrained minimization problem; rather, the task is to find a feasible point which is superior (with respect to an objective function value) to one returned by a feasibility-seeking only algorithm. We distinguish between two research directions in the superiorization methodology that nourish from the same general principle: Weak superiorization and strong superiorization and clarify their nature.

Weak and Strong Superiorization: Between Feasibility-Seeking and Minimization

Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 3498838,

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Weak and Strong Superiorization: Between Feasibility-Seeking and Minimization"}

We review the superiorization methodology, which can be thought of, in some cases, as lying between feasibility-seeking and constrained minimization. It is not...

Weak and Strong Superiorization: Between Feasibility-Seeking and Minimization

Published Online: Apr 22, 2017

Page range: 41 - 54

Received: Nov 01, 2014

Accepted: Feb 01, 2015

DOI: https://doi.org/10.1515/auom-2015-0046

Keywords
perturbation resilience, constrained minimization, convex feasibility problem, dynamic string-averaging, superiorization methodology, superiorized version of an algorithm, strict Fejér monotonicity

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Weak and Strong Superiorization: Between Feasibility-Seeking and Minimization

Published Online: Apr 22, 2017

Page range: 41 - 54

Received: Nov 01, 2014

Accepted: Feb 01, 2015

DOI: https://doi.org/10.1515/auom-2015-0046

Keywordsperturbation resilience, constrained minimization, convex feasibility problem, dynamic string-averaging, superiorization methodology, superiorized version of an algorithm, strict Fejér monotonicity

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
perturbation resilience, constrained minimization, convex feasibility problem, dynamic string-averaging, superiorization methodology, superiorized version of an algorithm, strict Fejér monotonicity