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The Criss-Cross Method for Solving Linear Programming Problems

1969; Institute for Operations Research and the Management Sciences; Volume: 15; Issue: 7 Linguagem: Inglês

10.1287/mnsc.15.7.426

1526-5501

Stanley Zionts,

Optimization and Variational Analysis

This paper 1 describes the Criss-Cross Method of solving linear programming problems. The method, a primal-dual scheme, normally begins with a problem solution that is neither primal nor dual feasible, and generates an optimal feasible solution in a finite number of iterations. Convergence of the method is proved and flow charts of the method are presented. The method has been programmed in FORTRAN and has been run on a number of computers including the IBM 1620, the IBM 7044, the CDC G-20, and the CDC 6400. A number of problems have been solved using the Criss-Cross method, and some comparisons between the Criss-Cross method and the Simplex method have been made. The results, though scanty, are favorable for the Criss-Cross method. A means of using the product form of the inverse with the Criss-Cross method is also discussed.