Abstract
In this paper, we propose a large-update primal-dual interior point algorithm for P*(κ)-linear complementarity problem. The method is based on a new class of kernel functions which is neither classical logarithmic function nor self-regular functions. It is determines both search directions and the proximity measure between the iterate and the center path. We show that if a strictly feasible starting point is available, then the new algorithm has \(o\left( {(1 + 2k)p\sqrt n {{\left( {\frac{1}{p}\log n + 1} \right)}^2}\log \frac{n}{\varepsilon }} \right)\) iteration complexity which becomes \(o\left( {(1 + 2k)\sqrt n log{\kern 1pt} {\kern 1pt} n\log \frac{n}{\varepsilon }} \right)\) with special choice of the parameter p. It is matches the currently best known iteration bound for P*(κ)-linear complementarity problem. Some computational results have been provided.
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The authors would like to deeply thank the referees for very valuable and helpful comments and suggestions, which made the paper more accurate and readable.
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Supported by Natural Science Foundation of China (Grant No.71471102).
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Ji, P., Zhang, Mw. & Li, X. A primal-dual large-update interior-point algorithm for P*(κ)-LCP based on a new class of kernel functions. Acta Math. Appl. Sin. Engl. Ser. 34, 119–134 (2018). https://doi.org/10.1007/s10255-018-0729-y
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DOI: https://doi.org/10.1007/s10255-018-0729-y