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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 $$o\left( {(1 + 2k)p\sqrt n {{\left( {\frac{1}{p}\log n + 1} \right)}^2}\log \frac{n}{\varepsilon }} \right)$$ o ( ( 1 + 2 k ) p n ( 1 p log n + 1 ) 2 log n ε ) iteration complexity which becomes $$o\left( {(1 + 2k)\sqrt n log{\kern 1pt} {\kern 1pt} n\log \frac{n}{\varepsilon }} \right)$$ o ( ( 1 + 2 k ) n l o g n log n ε ) 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.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Mar 8, 2018
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