Weak and Strong Superiorization: Between Feasibility-Seeking and Minimization

作者：Censor Yair

来源：Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, 2015, 23(3): 41-54.

DOI：10.1515/auom-2015-0046

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

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 fledged 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.

• 出版日期2015