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Abstract: In this paper we propose a new large-update primal-dual interior point algorithm for 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 LCPs. New search directions and proximity measures are proposed based on a kernel function which is not logarithmic barrier nor self-regular for LCPs. We showed that if a strictly feasible starting point is available, then the new large-update primal-dual interior point algorithm for solving LCPs has the polynomial complexity and gives a simple complexity analysis. This proximity function has not been used in the complexity analysis of interior point method (IPM) for LCPs before. [Copyright &y& Elsevier]

Abstract: In this paper we propose a new large-update primal-dual interior point algorithm for P ∗(κ) linear complementarity problems (LCPs). Recently, Peng et al. introduced self-regular barrier functions for primal-dual interior point methods (IPMs) for linear optimization (LO) problems and reduced the gap between the practical behavior of the algorithm and its theoretical worst case complexity. We introduce a new class of kernel functions which is not logarithmic barrier nor self-regular in the complexity analysis of interior point method (IPM) for P ∗(κ) linear complementarity problem (LCP). New search directions and proximity measures are proposed based on the kernel function. We showed that if a strictly feasible starting point is available, then the new large-update primal-dual interior point algorithms for solving P ∗(κ) LCPs have the polynomial complexity which is better than the classical large-update primal-dual algorithm based on the classical logarithmic barrier function. [Copyright &y& Elsevier]