Hybrid Approach with Active Set Identification for Mathematical Programs with Complementarity Constraints |
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Authors: | G H Lin M Fukushima |
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Institution: | (1) Department of Applied Mathematics, Dalian University of Technology, Dalian, China;(2) Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan |
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Abstract: | We consider a mathematical program with complementarity constraints (MPCC). Our purpose is to develop methods that enable
us to compute a solution or a point with some kind of stationarity to MPCC by solving a finite number of nonlinear programs.
We apply an active set identification technique to a smoothing continuation method (Ref. 1) and propose a hybrid algorithm
for solving MPCC. We develop also two modifications: one makes use of an index addition strategy; the other adopts an index
subtraction strategy. We show that, under reasonable assumptions, all the proposed algorithms possess a finite termination
property. Further discussions and numerical experience are given as well
This work was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science, Sports, and
Culture of Japan. The authors are grateful to Professor Paul Tseng for helpful suggestions on an earlier version of the paper. |
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Keywords: | Mathematical programs with complementarity constraints (MPCC) linear independence constraint qualification (LICQ) B-stationarity M-stationarity C-stationarity asymptotically weak nondegeneracy identification functions |
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