A non-interior continuation method for generalized linear complementarity problems |
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| Authors: | Ji-Ming Peng Zhenghua Lin |
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| Institution: | (1) State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific Computing, Academic Sinica, Beijing, P.O. Box 2719, China, 100080, Current address: Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 5031, 2628 CD, Mekelweg 4, Delft, The Netherlands, e-mail: j.peng@its.tudelft.nl, CN;(2) Department of Mathematics, Jilin University, Changchun 130023, P.R. China, CN |
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| Abstract: | In this paper, we propose a non-interior continuation method for solving generalized linear complementarity problems (GLCP)
introduced by Cottle and Dantzig. The method is based on a smoothing function derived from the exponential penalty function
first introduced by Kort and Bertsekas for constrained minimization. This smoothing function can also be viewed as a natural
extension of Chen-Mangasarian’s neural network smooth function. By using the smoothing function, we approximate GLCP as a
family of parameterized smooth equations. An algorithm is presented to follow the smoothing path. Under suitable assumptions,
it is shown that the algorithm is globally convergent and local Q-quadratically convergent. Few preliminary numerical results
are also reported.
Received September 3, 1997 / Revised version received April 27, 1999?Published online July 19, 1999 |
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| Keywords: | : generalized linear complementarity problem – non-interior continuation method – Newton method – Q-quadratical convergence Mathematics Subject Classification (1991): 90C33 |
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