ON FULLY SEMIMONOTONE MATRICES

G. S. R. Murthy (), T. Parthasarathy () and R. Sridhar ()
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G. S. R. Murthy: Statistical Quality Control and Operations Research, Indian Statistical Institute, Street No. 8, Habsiguda, Hyderabad 500007, Andhra Pradesh, India
T. Parthasarathy: Indian Statistical Institute, 37/110, Nelson Manicham Road, Chennai 600029, Tamil Nadu, India
R. Sridhar: Information Analytics, PD & GT, Caterpillar Inc, Peoria IL 61629, USA

International Game Theory Review (IGTR), 2013, vol. 15, issue 04, 1-17

Abstract: The class of fully semimonotone matrices is well known in the study of the linear complementarity problem. Stone [(1981) Ph.D. thesis, Dept. of Operations Research, Stanford University, Stanford, CA] introduced this class and conjectured that the principal minors of any fully semimonotoneQ0-matrix are non-negative. While the problem is still open, Murthy and Parthasarathy [(1998)Math. Program.82, 401–411] introduced the concept of incidence using which they proved that the principal minors of any matrix in the class of fully copositiveQ0-matrices, a subclass of fully semimonotoneQ0-matrices, are non-negative. In this paper, we study some properties of fully semimonotone matrices in connection with incidence. The main result of the paper shows that Stone's conjecture is true in the special case where the complementary cones have no partial incidence. We also present an interesting characterization ofQ0for matrices with a special structure. This result is very useful in checking whether a given matrix belongs toQ0provided it has the special structure. Several examples are discussed in connection with incidence andQ0property.

Keywords: Linear complementarity problem; fully semimonotone matrices; complementary cones; incidence; 90C33 (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 (1)

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DOI: 10.1142/S0219198913400367

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