Interior-point algorithms for $$P_{*}(\kappa )$$ -LCP based on a new class of kernel functions

Yong-Hoon Lee (), You-Young Cho () and Gyeong-Mi Cho ()

Journal of Global Optimization, 2014, vol. 58, issue 1, 137-149

Abstract: In this paper, we propose interior-point algorithms for $$P_* (\kappa )$$ -linear complementarity problem based on a new class of kernel functions. New search directions and proximity measures are defined based on these functions. We show that if a strictly feasible starting point is available, then the new algorithm has $$\mathcal{O }\bigl ((1+2\kappa )\sqrt{n}\log n \log \frac{n\mu ^0}{\epsilon }\bigr )$$ and $$\mathcal{O }\bigl ((1+2\kappa )\sqrt{n} \log \frac{n\mu ^0}{\epsilon }\bigr )$$ iteration complexity for large- and small-update methods, respectively. These are the best known complexity results for such methods. Copyright Springer Science+Business Media New York 2014

Keywords: Interior-point method; Kernel function; Complexity; Polynomial algorithm; Linear complementarity problem (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10898-013-0072-z

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