This paper studies the solution of two problems---bound-constrained quadratic programs and linear complementarity problems---by two-phase methods that consist of an active set prediction phase and a subspace phase. The algorithms enjoy favorable convergence properties under weaker assumptions than those assumed for other methods in the literature. The active set prediction phase employs matrix splitting iterations that are tailored to the structure of the (nonconvex) bound-constrained problems and the (asymmetric) linear complementarity problems studied in this paper. Numerical results on a variety of test problems illustrate the performance of the methods.
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