SOLVING STRONGLY MONOTONE LINEAR COMPLEMENTARITY PROBLEMS

A. Chandrashekaran (), T. Parthasarathy () and V. Vetrivel ()
Additional contact information
A. Chandrashekaran: School of Mathematics and Computer Science, Central University of Tamil Nadu, Thiruvarur-610 004, Tamil Nadu, India
T. Parthasarathy: Indian Statistical Institute, Chennai Centre, Chennai - 600 029, Tamil Nadu, India
V. Vetrivel: Department of Mathematics, Indian Institute of Technology Madras, Chennai - 600 036, Tamil Nadu, India

International Game Theory Review (IGTR), 2013, vol. 15, issue 04, 1-13

Abstract: Given a linear transformationLon a finite dimensional real inner product spaceVto itself and an elementq ∈ Vwe consider the general linear complementarity problemLCP(L, K, q)on a proper coneK ⊆ V. We observe that the iterates generated by any closed algorithmic map will converge to a solution forLCP(L, K, q), wheneverLis strongly monotone. Lipschitz constants ofLis vital in establishing the above said convergence. Hence we compute the Lipschitz constants for certain classes of Lyapunov, Stein and double-sided multiplicative transformations in the setting of semidefinite linear complementarity problems. We give a numerical illustration of a closed algorithmic map in the setting of a standard linear complementarity problem. On account of the difficulties in numerically implementing such algorithms for general linear complementarity problems, we give an alternative algorithm for computing the solution for a special class of strongly monotone semidefinite linear complementarity problems along with a numerical example.

Keywords: Complementarity problems; strongly monotone; Lipschitzian property; 22E46; 53C35; 57S20 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219198913400355
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:igtrxx:v:15:y:2013:i:04:n:s0219198913400355

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219198913400355

Access Statistics for this article

International Game Theory Review (IGTR) is currently edited by David W K Yeung

More articles in International Game Theory Review (IGTR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().