Can Linear Superiorization Be Useful for Linear Optimization Problems?

Abstract

Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? and (ii) How does linear superiorization fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: "yes" and "very well", respectively.

Inverse Problems, accepted for publication

References in corpus (3)

• Perturbation Resilience and Superiorization of Iterative Algorithms
• Projection Methods: An Annotated Bibliography of Books and Reviews
• Superiorization and Perturbation Resilience of Algorithms: A Continuously Updated Bibliography

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