Abstract
A gradient projection successive overrelaxation (GP-SOR) algorithm is proposed for the solution of symmetric linear complementary problems and linear programs. A key distinguishing feature of this algorithm is that when appropriately parallelized, the relaxation factor interval (0, 2) isnot reduced. In a previously proposed parallel SOR scheme, the substantially reduced relaxation interval mandated by the coupling terms of the problem often led to slow convergence. The proposed parallel algorithm solves a general linear program by finding its least 2-norm solution. Efficiency of the algorithm is in the 50 to 100 percent range as demonstrated by computational results on the CRYSTAL token-ring multicomputer and the Sequent Balance 21000 multiprocessor.
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This material is based on research supported by National Science Foundation Grants DCR-8420963 and DCR-8521228 and Air Force Office of Scientific Research Grants AFOSR-86-0172 and AFOSR-86-0255.
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Mangasarian, O.L., De Leone, R. Parallel gradient projection successive overrelaxation for symmetric linear complementarity problems and linear programs. Ann Oper Res 14, 41–59 (1988). https://doi.org/10.1007/BF02186473
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DOI: https://doi.org/10.1007/BF02186473