@MISC{Sturm_anapplication, author = {Jos Sturm}, title = {An Application Of Carver's Theorem To Monotone Linear Complementarity Problems}, year = {} }

Share

OpenURL

Abstract

h is sufficient for the boundedness of the solution set F , see Mangasarian [3]. Corollary 3 in Ye [6] states that the existence of such x and s is also necessary in the case of monotone LCPs with a so--called negative q--value. To see that it is necessary in general, suppose that there exist no such positive solution pair (x; s). Then, by Carver's theorem [1], there exists a direction u 6= 0 such that M T u 0; u 0; h T u 0: If h T u ! 0 then F = ;, by Farkas' lemma. Suppose now that there exist (x ; s ) 2 F , and consequently h T u = 0. Since u 0 and M T u 0, w