ISSN:
1573-2894
Keywords:
smoothing method
;
complexity bound
;
linear complementarity problem
;
monotonicity
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract We consider the standard linear complementarity problem (LCP): Find (x, y) ∈ R 2n such that y = M x + q, (x, y) ≥ 0 and x i y i = 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 P 0 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 $$O\left( {\frac{{\gamma ^{ - 6} n}}{{\varepsilon ^6 }}\log \frac{{\gamma ^{ - 2} n}}{{\varepsilon ^2 }}} \right)$$ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1026550331760
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