Error bounds for monotone linear complementarity problems

“…When problem (1) is monotone, the result of global s-type error bound was obtained by Mangasarian and Shiau [24], i.e., there is a positive number ρ which depends only on the data of problem (1) such that…”

Section: Thus A(x) ∪ B(x) = I and A(x) ∩ B(x) = ∅mentioning

confidence: 97%

New projection-type methods for monotone LCP with finite termination

Zhang

Xiu

2002

Numerische Mathematik

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In this paper we establish two new projection-type methods for the solution of monotone linear complementarity problem (LCP). The methods are a combination of the extragradient method and the Newton method, in which the active set strategy is used and only one linear system of equations with lower dimension is solved at each iteration. It is shown that under the assumption of monotonicity, these two methods are globally and linearly convergent. Furthermore, under a nondegeneracy condition they have a finite termination property. At last, the methods are extended to solving monotone affine variational inequality problem.Mathematics Subject Classification: 90C30, 90C33, 65K05

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“…To our knowledge, Mangasarian and Shiau ( [13]) are the first one who gave the solution structure and error estimation analysis to LCP. Latter, Mathias and Pang ( [14]) established the solution structure and global error estimation for the LCP with a P-matrix in terms of the natural residual function, and Mangasarian and Ren gave the same error estimation of the LCP with an 0 R -matrix in [15].…”

Section: G Xmentioning

confidence: 99%

“…In the end of this paper, we will consider a special case of GLCP which was discussed in [13,14,15,16]. Vol.…”

Section: Lemma 1 For Polyhedral Conementioning

confidence: 99%

The Solution Structure and Error Estimation for The Generalized Linear Complementarity Problem

Yan¹

2014

ijacsa

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Abstract-In this paper, we consider the generalized linear complementarity problem (GLCP). Firstly, we develop some equivalent reformulations of the problem under milder conditions, and then characterize the solution of the GLCP. Secondly, we also establish the global error estimation for the GLCP by weakening the assumption. These results obtained in this paper can be taken as an extension for the classical linear complementarity problems.

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Error bounds for monotone linear complementarity problems

Cited by 73 publications

References 2 publications

Local convergence of interior-point algorithms for degenerate monotone LCP

Local convergence of interior-point algorithms for degenerate monotone LCP

New projection-type methods for monotone LCP with finite termination

The Solution Structure and Error Estimation for The Generalized Linear Complementarity Problem

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