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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Improving the convergence
of non-interior point algorithms
for nonlinear complementarity problems


Authors: Liqun Qi and Defeng Sun
Journal: Math. Comp. 69 (2000), 283-304
MSC (1991): Primary 90C33; Secondary 90C30, 65H10
Published electronically: February 19, 1999
MathSciNet review: 1642766
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Abstract | References | Similar Articles | Additional Information

Abstract: Recently, based upon the Chen-Harker-Kanzow-Smale smoothing function and the trajectory and the neighbourhood techniques, Hotta and Yoshise proposed a noninterior point algorithm for solving the nonlinear complementarity problem. Their algorithm is globally convergent under a relatively mild condition. In this paper, we modify their algorithm and combine it with the superlinear convergence theory for nonlinear equations. We provide a globally linearly convergent result for a slightly updated version of the Hotta-Yoshise algorithm and show that a further modified Hotta-Yoshise algorithm is globally and superlinearly convergent, with a convergence $Q$-order $1+t$, under suitable conditions, where $t\in (0,1)$ is an additional parameter.


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Additional Information

Liqun Qi
Affiliation: School of Mathematics, The University of New South Wales, Sydney 2052, Australia
Email: L.Qi@unsw.edu.au

Defeng Sun
Affiliation: School of Mathematics, The University of New South Wales, Sydney 2052, Australia
Email: sun@maths.unsw.edu.au

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01082-0
PII: S 0025-5718(99)01082-0
Keywords: Nonlinear complementarity problem, noninterior point, approximation, superlinear convergence
Received by editor(s): June 9, 1997
Received by editor(s) in revised form: March 9, 1998
Published electronically: February 19, 1999
Additional Notes: This work is supported by the Australian Research Council.
Article copyright: © Copyright 1999 American Mathematical Society