Parallel and serial solution of large-scale linear complementarity problems
This thesis is concerned with developing algorithms for solving large-scale versions of the linear complementarity problem (LCP), which consists of finding an n-dimensional vector z such that z greater than or equal to O, Mz + q greater than or equal to O, and z(mz + q) = O where M is an n-by-n real matrix and q is a n-vector. The first algorithm proposed is an asynchronous parallel successive overrelaxation (SOR) algorithm suitable for large sparse symmetric problems. The second algorithm is a distributed version of Lemke's classical algorithm for solving the LCP. The algorithm is designed for a loosely-coupled network of computers. The third is a serial two-stage successive overrelaxation algorithm for the symmetric positive semidefinite LCP. This algorithm concentrates on updating a certain prescribed subset of variables which is determined by exploiting the complementarity property. It is demonstrated that this algorithm successfully solves problems with as many as 10,000 variables which cannot be tackled by other current algorithms. A fourth hybrid algorithm finds an exact solution for the positive definite symmetric linear complementarity problem in a finite number of steps. In this algorithm a successive overrelaxation preprocessing step is used.
- Research Organization:
- Wisconsin Univ., Madison (USA)
- OSTI ID:
- 7231022
- Country of Publication:
- United States
- Language:
- English
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