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A LOCALLY SMOOTHING METHOD FOR MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

Published online by Cambridge University Press:  27 March 2015

YU CHEN  and
ZHONG WAN
YU CHEN
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha, China email chenyu4660@163.com, wanmath@163.com School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
ZHONG WAN*
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha, China email chenyu4660@163.com, wanmath@163.com State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, China
*
✉wanmath@163.com
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Abstract

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We propose a locally smoothing method for some mathematical programs with complementarity constraints, which only incurs a local perturbation on these constraints. For the approximate problem obtained from the smoothing method, we show that the Mangasarian–Fromovitz constraints qualification holds under certain conditions. We also analyse the convergence behaviour of the smoothing method, and present some sufficient conditions such that an accumulation point of a sequence of stationary points for the approximate problems is a C-stationary point, an M-stationary point or a strongly stationary point. Numerical experiments are employed to test the performance of the algorithm developed. The results obtained demonstrate that our algorithm is much more promising than the similar ones in the literature.

Keywords

mathematical programs with complementarity constraintsconstraints qualificationconvergencestationary point

MSC classification

Primary: 90C30: Nonlinear programming
Secondary: 65K10: Optimization and variational techniques
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 3 , January 2015 , pp. 299 - 315
Copyright
© 2015 Australian Mathematical Society 

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