On the gradient-projection method for solving the nonsymmetric linear complementarity problem |
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Authors: | Y. C. Cheng |
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Affiliation: | (1) Department of Mathematics and Computer Science, University of Maryland Baltimore County, Catonsville, Maryland |
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Abstract: | The Levitin-Poljak gradient-projection method is applied to solve the linear complementarity problem with a nonsymmetric matrixM, which is either a positive-semidefinite matrix or aP-matrix. Further-more, if the quadratic functionxT(Mx + q) is pseudoconvex on the feasible region {x Rn |Mx + q 0,x0}, then the gradient-projection method generates a sequence converging to a solution, provided that the problem has a solution. For the case when the matrixM is aP-matrix and the solution is nondegenerate, the gradient-projection method is finite.This work is based on the author's PhD Dissertation, which was supported by NSF Grant No. MCS-79-01066 at the University of Wisconsin, Madison, Wisconsin.The author would like to thank Professor O. L. Mangasarian for his guidance of the dissertation. |
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Keywords: | Linear complementarity nonlinear programming gradient projection method |
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