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Can Linear Superiorization Be Useful for Linear Optimization Problems?

Yair Censor1

  • 1Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 3498838, Israel.

Inverse Problems
|January 17, 2018
PubMed
Summary
This summary is machine-generated.

Linear superiorization, a novel approach for linear programming, effectively finds feasible solutions with lower target function values compared to standard methods. It also performs competitively against the Simplex method.

Keywords:
Agmon-Motzkin-Schoenberg algorithmSimplex algorithmSuperiorizationalgorithmic operatorbounded perturbation resiliencefeasibility-seekinglinear feasibility problemlinear inequalitieslinear programminglinear superiorization

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Area of Science:

  • Operations Research
  • Computational Optimization

Background:

  • Linear programming (LP) problems are fundamental in optimization.
  • Traditional methods like the Simplex algorithm can be computationally intensive.
  • Superiorization offers an alternative paradigm for tackling optimization challenges.

Purpose of the Study:

  • To experimentally evaluate if linear superiorization yields better objective function values than standard feasibility-seeking algorithms.
  • To compare the performance of linear superiorization against the Simplex method for solving LP problems.

Main Methods:

  • Implementing perturbation-resilient feasibility-seeking algorithms.
  • Applying the superiorization technique to guide algorithms toward reduced target function values.
  • Conducting computational experiments to compare outcomes.

Main Results:

  • Linear superiorization successfully identified feasible points with lower linear target function values.
  • The approach demonstrated strong performance when compared to the Simplex method.

Conclusions:

  • Linear superiorization is a viable and effective method for linear programming.
  • It offers a promising alternative for finding improved solutions in optimization problems.