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

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## 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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