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Annals of Operations Research

, Volume 258, Issue 2, pp 587–612 | Cite as

A comparative note on the relaxation algorithms for the linear semi-infinite feasibility problem

  • A. Ferrer
  • M. A. Goberna
  • E. González-Gutiérrez
  • M. I. TodorovEmail author
S.I. : CLAIO 2014

Abstract

The problem (LFP) of finding a feasible solution to a given linear semi-infinite system arises in different contexts. This paper provides an empirical comparative study of relaxation algorithms for (LFP). In this study we consider, together with the classical algorithm, implemented with different values of the fixed parameter (the step size), a new relaxation algorithm with random parameter which outperforms the classical one in most test problems whatever fixed parameter is taken. This new algorithm converges geometrically to a feasible solution under mild conditions. The relaxation algorithms under comparison have been implemented using the extended cutting angle method for solving the global optimization subproblems.

Keywords

Linear semi-infinite systems Feasibility problem Relaxation method Cutting angle method 

Notes

Acknowledgments

The authors are grateful to the referees for their constructive comments and helpful suggestions which have contributed to the final preparation of the paper.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • A. Ferrer
    • 1
  • M. A. Goberna
    • 2
  • E. González-Gutiérrez
    • 3
  • M. I. Todorov
    • 4
    Email author
  1. 1.Departament de Matemàtica Aplicada IUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Department of Statistics and Operations ResearchAlicante UniversityAlicanteSpain
  3. 3.School of EngineeringPolytechnic University of TulancingoHidalgoMexico
  4. 4.Department of Physics and MathematicsUDLAPPueblaMexico

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