New error bounds for the extended vertical LCP

Abstract

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.