A non-interior-point continuation method for linear complementarity problems
SIAM Journal on Matrix Analysis and Applications
Mathematics of Operations Research
Existence and Limiting Behavior of Trajectories Associatedwith P0-equations
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Complexity of a noninterior path-following method for the linear complementarity problem
Journal of Optimization Theory and Applications
A Complexity Bound of a Predictor-Corrector Smoothing Method Using CHKS-Functions for Monotone LCP
Computational Optimization and Applications
Computational Optimization and Applications
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We consider the standard linear complementarity problem (LCP): Find (x, y) ∈ R2n such that y = Mx + q, (x, y) ≥ 0 and xiyi = 0 (i = 1, 2, … , n), where M is an n × n matrix and q is an n-dimensional vector. Recently several smoothing methods have been developed for solving monotone and/or P0 LCPs. The aim of this paper is to derive a complexity bound of smoothing methods using Chen-Harker-Kanzow-Smale functions in the case where the monotone LCP has a feasible interior point. After a smoothing method is provided, some properties of the CHKS-function are described. As a consequence, we show that the algorithm terminates in O (\frac{\bar{\gamma}^{6}n}{\epsilon^6} \hbox{ log }\frac{\bar{\gamma}^2n}{\epsilon^2}) Newton iterations where \bar{\gamma} is a number which depends on the problem and the initial point. We also discuss some relationships between the interior point methods and the smoothing methods.