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A Note on P1 - and Lipschitzian Matrices

2000
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SIAM Journal on Matrix Analysis and Applications
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The linear complementarity problem (q, A) with data A ∈ R n×n and q ∈ R n involves finding a nonnegative z ∈ R n such that Az + q ≥ 0 and z t (Az + q) = 0. Cottle and Stone introduced the class of P 1 -matrices and showed that if A is in P 1 \Q, then K(A) (the set of all q for which (q, A) has a solution) is a half-space and (q, A) has a unique solution for every q in the interior of K(A). Extending the results of Murthy, Parthasarathy, and Sriparna [Ann. Dynamic Games, to appear], we present a

doi:10.1137/s0895479897329898
fatcat:u24eehujlbby7doadeeeqiqi7i