Perturbation Resilience and Superiorization of Iterative Algorithms

Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little demand on computer resources. For other problems, such as finding that point in the intersection at which the value of a given function is optimal, algorithms tend to need more computer memory and longer execution time. A methodology is presented whose aim is to produce automatically for an iterative algorithm of the first kind a "superiorized version" of it that retains its computational efficiency but nevertheless goes a long way towards solving an optimization problem. This is possible to do if the original algorithm is "perturbation resilient," which is shown to be the case for various projection algorithms for solving the consistent convex feasibility problem. The superiorized versions of such algorithms use perturbations that ...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Yair Censor, R. Davidi, Gabor T. Herman
• Keywords: Algorithms, CORR 2010, Education, Iterative Algorithm, Superiorized Versions