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Two direct methods in linear programming. (English) Zbl 0991.90087
Summary: We introduce two direct methods for solving some classes of linear programming problems. The first method produces the extreme vertex or a neighboring vertex with respect to the extreme point. The second method is based on the game theory. Both these methods can be used in the preparation of the starting point for the simplex method. The efficiency of the improved simplex method, whose starting point is constructed by these introduced methods, is compared with the original simplex method and the interior point methods, and illustrated by examples. Also, we investigate the elimination of excessive constraints.
MSC:
90C05Linear programming
90C49Extreme-point and pivoting methods
90C51Interior-point methods
91A90Experimental studies in game theory