Global error bounds for the extended vertical LCP

Zhang, Chao; Chen, Xiaojun; Xiu, Naihua

doi:10.1007/s10589-007-9134-9

Cited by 12 publications

(28 citation statements)

References 15 publications

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“…Then, based on this, some new error bounds for the EVLCP (A, q) are obtained. Not only that, these new error bounds cover some existing results in [18] and [19] as well. Meanwhile, it avoids the row rearrangement of the system matrix A. Incidentally, for the row W-property, two new sufficient and necessary conditions are given.…”

Section: Introductionsupporting

confidence: 67%

“…n times to obtain α(A). Therefore, the calculation times of Theorem 4.1 in [19] for k = 1 achieve at most 2 n times. Whereas, the calculation time of Theorem 3.1 in [19] is 1.…”

Section: Old Error Boundmentioning

confidence: 97%

“…. , A k ) has the row W-property (see the following definition), Zhao et al in [19] presented the following result,…”

Section: Introductionmentioning

confidence: 99%

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New error bounds for the extended vertical LCP

Wu¹,

Wang²

2022

Preprint

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In this paper, by making use of the equality minwith a j , b j , λ j ∈ R, λ j ∈ [0, 1] and n j=1 λ j = 1, some new error bounds of the extended vertical LCP under the row W-property are obtained, which cover the error bounds in [Math. Program., 106 (2006) 513-525] by Chen and Xiang, and [Comput. Optim. Appl., 42 (2009) 335-352] by Zhang, Chen and Xiu. Not only that, these new error bounds skillfully avoid that the inconvenience is caused by the row rearrangement technique for error bounds, which was introduced in the latter paper mentioned above. Besides, with respect to the row W-property, two new sufficient and necessary conditions are obtained.

show abstract

Section: Introductionsupporting

confidence: 67%

“…n times to obtain α(A). Therefore, the calculation times of Theorem 4.1 in [19] for k = 1 achieve at most 2 n times. Whereas, the calculation time of Theorem 3.1 in [19] is 1.…”

Section: Old Error Boundmentioning

confidence: 97%

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New error bounds for the extended vertical LCP

Wu¹,

Wang²

2022

Preprint

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“…Compared with the error bounds established in [ 4 , 20 – 23 ], we remove the assumptions such as monotonicity, positive semidefiniteness, and so on.…”

Section: Global Error Bound For Special Cases Of Elcpmentioning

confidence: 99%

New global error bound for extended linear complementarity problems

Sun

Wang

2018

J Inequal Appl

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For the extended linear complementarity problem (ELCP), by virtue of a new residual function, we establish a new type of global error bound under weaker conditions. Based on this, we respectively obtain new global error bounds for the vertical linear complementarity problem and the mixed linear complementarity problem. The obtained results presented in this paper supplement some recent corresponding results in the sense that they can provide some error bounds for a more general ELCP. Their feasibility is verified by some numerical experiments.

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“…Error bounds for the LCP(q, M) have been studied extensively by using the natural residual min(x, Mx + q), see [1,2,5,8,9,15,19,24,30,31,34,38,45,46,48]. In the following, we give sharper global error bounds for an approximate solution of the following system of nonsmooth equations…”

Section: Global Error Boundsmentioning

confidence: 99%