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A KRYLOV SUBSPACE METHOD FOR LARGE-SCALE SECOND-ORDER CONE LINEAR COMPLEMENTARITY PROBLEM
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DOI：10.1137/140995064.png)
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In this paper, we first show that the second-order cone linear complementarity problem (SOCLCP) can be solved by finding a positive zero s* is an element of R of a particular rational function h(s), and we then propose a Krylov subspace method to reduce h(s) to h(l) (s) as in the model reduction. The zero s* of h(s) can be accurately approximated by that of h(l) (s) = 0, which itself can be cast as a small eigenvalue problem. The new method is made possible by a complete characterization of the curve of h(s), and it has several advantages over the bisection-Newton (BN) iteration recently proposed by [L.-H. Zhang and W. H. Yang, Math. Comp., 83 (2013), pp. 1701-1720] and shown to be very efficient for small-to medium-size problems. The method is tested and compared against the BN iteration and two other state-of-the-art packages: SDPT3 and SeDuMi. Our numerical results show that the method is very efficient for both small to medium dense problems and large-scale ones.
Keyword:
second-order cone
linear complementarity problem
SOCLCP
globally uniquely solvable property
GUS
Krylov subspace
model reduction
linear complementarity problem via Arnoldi process
LCPvA
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