(untitled) (Journal of Computational Mathematics, 1991)
In this paper the following canonical form of a general LP problem, max Z=C^TX, subject to AX≥ bis considered for XR^n. The constraints form an arbitrary convex polyhedron Ω^m in R^n. In Ω^m a strictly interior point is successively moved to a higher isometric plane from a lower one along the gradient function value maximum is found or the infinite value of the objective function is concluded. For an m* n matrix A the arithmetic operations of a movement are O(mn) in our algorithm. The algorithm enables one to solve linear equations with ill conditions as well as a general LP problem. Some interesting examples illustrate the efficiency of the algorithm.