Kernel-Based Interior-Point Methods for Monotone Linear Complementarity Problems over Symmetric Cones

被引:16
|
作者
Lesaja, G. [1 ]
Roos, C. [2 ]
机构
[1] Georgia So Univ, Dept Math Sci, Statesboro, GA 30460 USA
[2] Delft Univ Technol, Fac Elect Engn Math & Comp Sci, NL-2600 GA Delft, Netherlands
关键词
Linear complementarity problem; Euclidean Jordan algebras and symmetric cones; Interior-point method; Kernel functions; Polynomial complexity; JORDAN ALGEBRAS; SEARCH DIRECTIONS; WIDE NEIGHBORHOOD; UNIFIED ANALYSIS; DUAL ALGORITHMS; CONVERGENCE; PATH;
D O I
10.1007/s10957-011-9848-9
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
We present an interior-point method for monotone linear complementarity problems over symmetric cones (SCLCP) that is based on barrier functions which are defined by a large class of univariate functions, called eligible kernel functions. This class is fairly general and includes the classical logarithmic function, the self-regular functions, as well as many non-self-regular functions as special cases. We provide a unified analysis of the method and give a general scheme on how to calculate the iteration bounds for the entire class. We also calculate the iteration bounds of both large-step and short-step versions of the method for ten frequently used eligible kernel functions. For some of them we match the best known iteration bound for large-step methods, while for short-step methods the best iteration bound is matched for all cases. The paper generalizes results of Lesaja and Roos (SIAM J. Optim. 20(6):3014-3039, 2010) from P (au)(kappa)-LCP over the non-negative orthant to monotone LCPs over symmetric cones.
引用
收藏
页码:444 / 474
页数:31
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