NEW COMPLEXITY ANALYSIS OF PRIMAL-DUAL IMPS FOR P* LAPS BASED ON LARGE UPDATES

Title & Authors
NEW COMPLEXITY ANALYSIS OF PRIMAL-DUAL IMPS FOR P* LAPS BASED ON LARGE UPDATES
Cho, Gyeong-Mi; Kim, Min-Kyung;

Abstract
In this paper we present new large-update primal-dual interior point algorithms for $\small{P_*}$ linear complementarity problems(LAPS) based on a class of kernel functions, $\small{{\psi}(t)={\frac{t^{p+1}-1}{p+1}}+{\frac{1}{\sigma}}(e^{{\sigma}(1-t)}-1)}$, p $\small{\in}$ [0, 1], $\small{{\sigma}{\geq}1}$. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for $\small{P_*}$ LAPS. We showed that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for $\small{P_*}$ LAPS have $\small{O((1+2+\kappa)n^{{\frac{1}{p+1}}}lognlog{\frac{n}{\varepsilon}})}$ complexity bound. When p = 1, we have $\small{O((1+2\kappa)\sqrt{n}lognlog\frac{n}{\varepsilon})}$ complexity which is so far the best known complexity for large-update methods.
Keywords
primal-dual interior point method;kernel function;complexity;polynomial algorithm;large-update;linear complementarity;path-following;
Language
Korean
Cited by
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