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

Authors:
Yong-Hoon Lee;You-Young Cho;Gyeong-Mi Cho
Affiliations:
Department of Mathematics, Pusan National University, Busan, Korea 609-735;Department of Mathematics, Pusan National University, Busan, Korea 609-735;Department of Software Engineering, Dongseo University, Busan, Korea 617-716
Venue:
Journal of Global Optimization
Year:
2014

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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.