## Abstract

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 only algorithm. Our main result reveals new information about the mathematical behavior of the superiorization methodology. We deal with a constrained minimization problem with a feasible region, which is the intersection of finitely many closed convex constraint sets, and use the dynamic string-averaging projection method, with variable strings and variable weights, as a feasibility-seeking algorithm. We show that any sequence, generated by the superiorized version of a dynamic string-averaging projection algorithm, not only converges to a feasible point but, additionally, also either its limit point solves the constrained minimization problem or the sequence is strictly Fejér monotone with respect to a subset of the solution set of the original problem.

Original language | English |
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Pages (from-to) | 172-187 |

Number of pages | 16 |

Journal | Journal of Optimization Theory and Applications |

Volume | 165 |

Issue number | 1 |

DOIs | |

State | Published - 6 Apr 2015 |

### Bibliographical note

Funding Information:This research project was supported by and Immigrant Absorption. The authors are editorial assistance.

Publisher Copyright:

© 2014, Springer Science+Business Media New York.

## Keywords

- Bounded perturbation resilience
- Constrained minimization
- Convex feasibility problem
- Dynamic string-averaging projections
- Strict Fejér monotonicity
- Subgradients
- Superiorization methodology
- Superiorized version of an algorithm

## ASJC Scopus subject areas

- Management Science and Operations Research
- Control and Optimization
- Applied Mathematics