A new interior-point algorithm for -NCP based on a class of parametric kernel functions

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• 作者：Xin Li ^{sxlixin12@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonlinear complementarity problem ; Interior point methods ; Kernel function ; Iteration complexity
• 刊名：Operations Research Letters
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：44
• 期：4
• 页码：463-468
• 全文大小：414 K

文摘

In this paper, we propose a long step interior point algorithm for solving the P_∗(k)$P_{\ast }\left(k\right)$-nonlinear complementarity problem (NCP) based on a new class of parametric kernel functions. A simple analysis shows that if a strictly feasible starting point is available and the problem satisfies certain conditions, then the proposed algorithm has $O((1+2k)\sqrt{n}lognlog(n{\mu }^0/\epsilon ))$ iteration complexity. This result coincides with the current best-known iteration bounds for such methods.