Abstract

In the paper a method is presented which evaluates a solution of a linear programming problem. From the parameters of primal and dual program a symmetric matrix game is constructed. The search for the solution of this game is reduced to a problem of the constrained convex minimization, where the minimized function is the maximum of finite number of affine functions and a standard simplex is the feasible region and the minimal value of the function is known. The subgradient method of Polyak is applied to solve this problem. The algorithm converges geometrically. On each iteration the projection onto a standard simplex is applied, for which a combinatorial algorithm is presented.

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