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.
Keywords: Superiorization, bounded perturbation resilience, linear superiorization, linear programming, Simplex algorithm, feasibility-seeking, algorithmic operator, Agmon-Motzkin-Schoenberg algorithm, linear inequalities, linear feasibility problem.
Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )
Category 2: Optimization Software and Modeling Systems (Problem Solving Environments )
Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )
Citation: Inverse Problems, accepted for publication.
Entry Submitted: 10/06/2016
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