A generalized projection-based scheme for solving convex constrained optimization problems

A generalized projection-based scheme for solving convex constrained optimization problems In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility problems by iteratively constraining the objective function from above until the feasibility problem is inconsistent. For each of the feasibility problems one may apply any of the existing projection methods for solving it. In particular, the scheme allows the use of subgradient projections and does not require exact projections onto the constraints sets as in existing similar methods. We also apply the newly introduced concept of superiorization to optimization formulation and compare its performance to our scheme. We provide some numerical results for convex quadratic test problems as well as for real-life optimization problems coming from medical treatment planning. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Optimization and Applications Springer Journals

A generalized projection-based scheme for solving convex constrained optimization problems

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Optimization; Operations Research, Management Science; Operations Research/Decision Theory; Statistics, general; Convex and Discrete Geometry
ISSN
0926-6003
eISSN
1573-2894
D.O.I.
10.1007/s10589-018-9991-4
Publisher site
See Article on Publisher Site

Abstract

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility problems by iteratively constraining the objective function from above until the feasibility problem is inconsistent. For each of the feasibility problems one may apply any of the existing projection methods for solving it. In particular, the scheme allows the use of subgradient projections and does not require exact projections onto the constraints sets as in existing similar methods. We also apply the newly introduced concept of superiorization to optimization formulation and compare its performance to our scheme. We provide some numerical results for convex quadratic test problems as well as for real-life optimization problems coming from medical treatment planning.

Journal

Computational Optimization and ApplicationsSpringer Journals

Published: Mar 2, 2018

References

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