Error bounds for nondegenerate monotone linear complementarity problems |
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Authors: | O L Mangasarian |
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Institution: | (1) Computer Sciences Department, University of Wisconsin, 53706 Madison, WI, USA |
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Abstract: | Error bounds and upper Lipschitz continuity results are given for monotone linear complementarity problems with a nondegenerate solution. The existence of a nondegenerate solution considerably simplifies the error bounds compared with problems for which all solutions are degenerate. Thus when a point satisfies the linear inequalities of a nondegenerate complementarity problem, the residual that bounds the distance from a solution point consists of the complementarity condition alone, whereas for degenerate problems this residual cannot bound the distance to a solution without adding the square root of the complementarity condition to it. This and other simplified results are a consequence of the polyhedral characterization of the solution set as the intersection of the feasible region {zMz + q 0, z 0} with a single linear affine inequality constraint.This material is based on research supported by National Science Foundation Grants CCR-8723091 and DCR-8521228 and Air Force Office of Scientific Research Grant AFOSR-86-0172. |
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Keywords: | Linear complementarity error bounds Lipschitz continuity |
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