| Résumé | Two new algorithms for solving the overdetermined system of linear inequalities Ca > 0 are presented. The first algorithm calculates the one-sided Chebyshev solution from below, of the overdetermined system of linear equations Ca = f, where f is a positive vector. The second algorithm calculates the one-sided L-one solution from below, of the same system, Ca = f. If a solution exists to either of the one-sided problems, it would be a solution to the given inequality Ca > 0. The algorithms converge in a finite number of steps. Also for infeasible solutions, the inequalities which cause the infeasibility are detected by the algorithms and best possible solutions are obtained. Finally, matrix C need not be of full rank. The present algorithms compare favourably with other known methods. Numerical results and comments are given. |
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