A new large - update interior point algorithm for P ∗ ( ) linear complementarity problems
نویسنده
چکیده
In this paper we propose a new large-update primal-dual interior point algorithm for P∗( ) linear complementarity problems (LCPs). We generalize Bai et al.’s [A primal-dual interior-point method for linear optimization based on a new proximity function, Optim. Methods Software 17(2002) 985–1008] primal-dual interior point algorithm for linear optimization (LO) problem to P∗( ) LCPs. New search directions and proximity measures are proposed based on a kernel function which is not logarithmic barrier nor self-regular for P∗( ) LCPs. We showed that if a strictly feasible starting point is available, then the new large-update primaldual interior point algorithm for solving P∗( ) LCPs has the polynomial complexity O((1+ 2 )n3/4 log(n/ )) and gives a simple complexity analysis. This proximity function has not been used in the complexity analysis of interior point method (IPM) for P∗( ) LCPs before. © 2007 Elsevier B.V. All rights reserved. MSC: 49M15; 65K05; 90C33
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