Mathematical Programming

, Volume 48, Issue 1–3, pp 437–445

# Error bounds for nondegenerate monotone linear complementarity problems

• O. L. Mangasarian
Article

## 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 {z∣Mz + q ≥ 0, z ≥ 0} with a single linear affine inequality constraint.

## Key words

Linear complementarity error bounds Lipschitz continuity

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© The Mathematical Programming Society, Inc. 1990

## Authors and Affiliations

• O. L. Mangasarian
• 1
1. 1.Computer Sciences DepartmentUniversity of WisconsinMadisonUSA

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