Resumen de Relaxation methods for solving linear inequality systems: converging results

E. González Gutiérrez, Lidia Aurora Hernández Rebollar, Maxim I. Todorov

• The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In González-Gutiérrez and Todorov (Optim. Lett. doi: 10.1007/s11590-010-0244-4, 2011), an algorithm, called extended relaxation method, for solving 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.