New Primal-dual Interior Point Methods for P∗(κ) Linear Complementarity Problems
نویسندگان
چکیده
In this paper we propose new primal-dual interior point methods (IPMs) for P∗(κ) linear complementarity problems (LCPs) and analyze the iteration complexity of the algorithm. New search directions and proximity measures are defined based on a class of kernel functions, ψ(t) = t 2−1 2 − R t 1 e q “ 1 ξ −1 ” dξ, q ≥ 1. If a strictly feasible starting point is available and the parameter q = log „ 1 + a q 2τ+2 √ 2nτ+θn 1−θ « , where a = 1 + 1 √ 1+2κ , then new large-update primal-dual interior point algorithms have O((1 + 2κ) √ n logn log n ε ) iteration complexity which is the best known result for this method. For small-update methods, we have O((1 + 2κ)q √ qn log n ε ) iteration complexity.
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