A Regularized Jacobi Method for Large-Scale Linear Programming

Kallio, M.J., Ruszczynski, A., & Salo, S. (1993). A Regularized Jacobi Method for Large-Scale Linear Programming. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-93-061

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Abstract

A parallel algorithm based on Jacobi iterations is proposed to minimize the augmented Lagrangian functions of the multiplier method for large-scale linear programming. Sparsity is efficiently exploited for determining stepsizes (column-wise) for the Jacobi iterations. Linear convergence is shown with convergence ratio depending on sparsity but not on the penalty parameter and on problem size. Employing simulation of parallel computations, an experimental code is tested extensively on 68 Netlib problems. Results are compared with the simplex method, an interior point algorithm and a Gauss-Seidel approach. We observe that speedup against the simplex method generally increases with the problem size, while the parallel solution times increase slowly, if at all. Our preliminary results compared with the other two methods are highly encouraging as well.

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