FAN,KY N-MATRICES AND LINEAR COMPLEMENTARITY-PROBLEMS

Authors
MIAO JM
Citation
Jm. Miao, FAN,KY N-MATRICES AND LINEAR COMPLEMENTARITY-PROBLEMS, Mathematical programming, 61(3), 1993, pp. 351-356
Citations number
14
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science",Mathematics,"Computer Applications & Cybernetics
Journal title
Mathematical programming → ACNP
ISSN journal
00255610
Volume
61
Issue
3
Year of publication
1993
Pages
351 - 356
Database
ISI
SICI code
0025-5610(1993)61:3<351:FNALC>2.0.ZU;2-G
Abstract
We consider the linear complementarity problem (LCP), w = Az+q, W grea ter-than-or-equal-to 0, Z greater-than-or-equal-to 0, W(T)Z = 0, when all the off-diagonal entries of A are nonpositive (the class of Z-matr ices), all the proper principal minors of A are positive and the deter minant of A is negative (the class of almost P-matrices). We shall cal l this the class of F-matrices. We show that if A is a Z-matrix, then A is an F-matrix if and only if LCP(q, A) has exactly two solutions fo r any q greater-than-or-equal-to 0, q not-equal 0, and has at most two solutions for any other q.