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On the Lipschitz continuity of the solution map in linear complementarity problems over second-order cone
Published in Elsevier Inc.
2016
Volume: 510
   
Pages: 146 - 159
Abstract
Let K⊆IRn denote the second-order cone. Given an n×n real matrix M and a vector q∈IRn, the second-order cone linear complementarity problem SOLCP(M,q) is to find a vector x∈IRn such thatx∈K,y:=Mx+q∈KandyTx=0. We say that M∈Q if SOLCP(M,q) has a solution for all q∈IRn. An n×n real matrix A is said to be a Z-matrix with respect to K iff:x∈K,y∈KandxTy=0 ⟹xTMy≤0. Let ΦM(q) denote the set of all solutions to SOLCP(M,q). The following results are shown in this paper: • If M∈Z∩Q, then ΦM is Lipschitz continuous if and only if M is positive definite on the boundary of K.• If M is symmetric, then ΦM is Lipschitz continuous if and only if M is positive definite. © 2016 Elsevier Inc.
About the journal
JournalData powered by TypesetLinear Algebra and Its Applications
PublisherData powered by TypesetElsevier Inc.
ISSN00243795
Open AccessNo
Concepts (11)
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    Linear algebra
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    Mathematical techniques
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    All solutions
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    Linear complementarity problems
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    Lipschitz continuity
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    LIPSCHITZ CONTINUOUS
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    Positive definite
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    REAL MATRICES
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    SECOND ORDER CONE
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    Z MATRIX
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    Matrix algebra