Parallel multisplittings for optimization

The philosophy of multisplitting methods is the replacement of a large-scale linear or nonlinear problem by a set of subproblems, each of which can be solved locally and independently in parallel by taking advantage of well-tested sequential algorithms. Because of this formulation most compute-intensive operations can be calculated independently and the algorithms are highly parallel. Recent developments for optimization, constrained and unconstrained, arc described. These new algorithms arc, in some cases, faster in sequential mode than conventional algorithms. Results of implementations on the Intel Paragon and on a cluster of workstations using PVM3 demonstrate superlinear speedup when compared with a standard test algorithm programmed in sequential mode. Further, the same algorithm when programmed in sequential mode also exhibits speedup when compared to the non-split algorithm.