TY - JOUR

T1 - Sign-solvable linear complementarity problems

AU - Kakimura, Naonori

N1 - Funding Information:
The author is very obliged to Satoru Iwata for his suggestions and reading the draft of the paper. This work is supported by the 21st Century COE Program on Information Science and Technology Strategic Core at the University of Tokyo from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

PY - 2008/7/15

Y1 - 2008/7/15

N2 - This paper presents a connection between qualitative matrix theory and linear complementarity problems (LCPs). An LCP is said to be sign-solvable if the set of the sign patterns of the solutions is uniquely determined by the sign patterns of the given coefficients. We provide a characterization for sign-solvable LCPs such that the coefficient matrix has nonzero diagonals, which can be tested in polynomial time. This characterization leads to an efficient combinatorial algorithm to find the sign pattern of a solution for these LCPs. The algorithm runs in O (γ) time, where γ is the number of the nonzero coefficients.

AB - This paper presents a connection between qualitative matrix theory and linear complementarity problems (LCPs). An LCP is said to be sign-solvable if the set of the sign patterns of the solutions is uniquely determined by the sign patterns of the given coefficients. We provide a characterization for sign-solvable LCPs such that the coefficient matrix has nonzero diagonals, which can be tested in polynomial time. This characterization leads to an efficient combinatorial algorithm to find the sign pattern of a solution for these LCPs. The algorithm runs in O (γ) time, where γ is the number of the nonzero coefficients.

KW - Linear complementarity problems

KW - Qualitative matrix theory

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U2 - 10.1016/j.laa.2008.03.022

DO - 10.1016/j.laa.2008.03.022

M3 - Article

AN - SCOPUS:43549124742

SN - 0024-3795

VL - 429

SP - 606

EP - 616

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 2-3

ER -