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Immunity to Increasing Condition Numbers of Linear Superiorization versus Linear Programming.

Jan Schröder¹, Yair Censor², Philipp Süss¹

¹Optimization Department, Fraunhofer - ITWM, Kaiserslautern 67663, Germany.

|August 7, 2024

Summary

This summary is machine-generated.

Linear Programming (LP) and Linear Superiorization (LinSup) algorithms were compared for their sensitivity to condition numbers. LinSup demonstrated better resilience to ill-posed problems compared to LP.

Keywords:

Condition number Gurobi Linear Programming Linear Superiorization Scipy bounded perturbations feasibility seeking ill-posed problem

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Area of Science:

Optimization Algorithms
Numerical Analysis
Computational Mathematics

Background:

Linear Programming (LP) finds optimal solutions under constraints.
Linear Superiorization (LinSup) seeks feasible solutions with reduced objective values.
Previous research compared LP and LinSup outputs and resource usage.

Purpose of the Study:

To investigate the sensitivity of LP and LinSup algorithms to condition numbers in linear constraint systems.
To evaluate the performance of LP and LinSup when dealing with ill-posed problems.

Main Methods:

Experimental investigation of LP and LinSup algorithms.
Analysis of algorithm performance on exemplary linear programming problems with varying condition numbers and dimensions.

Main Results:

The study experimentally assessed the advantages and disadvantages of both LP and LinSup.
Sensitivity to condition numbers was a key focus of the experimental analysis.

Conclusions:

The paper provides insights into the robustness of LP and LinSup concerning problem condition numbers.
This research addresses a previously unstudied aspect of comparing LP and LinSup methodologies.