TY - JOUR

T1 - Some n by dn linear complementarity problems

AU - Kaneko, Ikuyo

AU - Pang, Jong Shi

N1 - Funding Information:
*The Research of this author is supported, in part, by the National Science Foundation under Grant No. ENC77-11136. ‘The research of this author is performed as a Part of the activities of the Management Science R esearch Group at Carnegie-Mellon University under contract N99914-7544621 with the Office of Naval Research.

PY - 1980/12

Y1 - 1980/12

N2 - The purpose of this paper is to study some recent applications of the n by dn LCP solvable by a parametric principal pivoting algorithm (PPP algorithm). Often, the LCPs arising from these applications give rise to large systems of linear equations which can be solved fairly efficiently by exploiting their special structures. First, it is shown that by analyzing the n by dn LCP we could study the problem of solving a system of equations and the (nonlinear) complementarity problem when the function involved is separable. Next, we examine conditions under which the PPP algorithm is applicable to a general LCP, and then present examples of LCPs arising from various applications satisfying the conditions; included among them is the n by dn LCP with a certain P-property. Finally we study a special class of n by dn LCPs which do not possess the P-property but to which the PPP algorithm is still applicable; a major application of this class of problems is a certain economic spatial equilibrium model with piecewise linear prices.

AB - The purpose of this paper is to study some recent applications of the n by dn LCP solvable by a parametric principal pivoting algorithm (PPP algorithm). Often, the LCPs arising from these applications give rise to large systems of linear equations which can be solved fairly efficiently by exploiting their special structures. First, it is shown that by analyzing the n by dn LCP we could study the problem of solving a system of equations and the (nonlinear) complementarity problem when the function involved is separable. Next, we examine conditions under which the PPP algorithm is applicable to a general LCP, and then present examples of LCPs arising from various applications satisfying the conditions; included among them is the n by dn LCP with a certain P-property. Finally we study a special class of n by dn LCPs which do not possess the P-property but to which the PPP algorithm is still applicable; a major application of this class of problems is a certain economic spatial equilibrium model with piecewise linear prices.

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U2 - 10.1016/0024-3795(80)90170-6

DO - 10.1016/0024-3795(80)90170-6

M3 - Article

AN - SCOPUS:49149149082

SN - 0024-3795

VL - 34

SP - 297

EP - 319

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -