The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. We consider solving linear semi-infinite inequality systems via an extension of the relaxation method for finite linear inequality systems. The difficulties are discussed and a convergence result is derived under fairly general assumptions on a large class of linear semi-infinite inequality systems.
The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we consider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.
The problem (LF P ) 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 (LF P ). 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 (ECAM) for solving the global optimization subproblems.
The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In E. Gonza´lez-Gutie´rrez and M.I. Todorov [A relaxation method for solving systems with infinitely many linear inequalities, Optim. Lett. ] an algorithm, called extended relaxation method (ERM), which solves the feasibility problem has been proposed. Later in E. Gonza´lez-Gutie´rrez, L. Herna´ndez Rebollar, and M.I. Todorov [Relaxation methods for solving linear inequality systems: Converging results, preprint, CMR, 990 (2011), pp. 1-9], we consider a class of algorithms, depending on a parameter and prove their convergence. In this article, for the same class of the ERMs a linear rate of convergence is obtained.
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