April  2013, 9(2): 305-322. doi: 10.3934/jimo.2013.9.305

Globally convergent algorithm for solving stationary points for mathematical programs with complementarity constraints via nonsmooth reformulations

1. 

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

2. 

School of Management, Shanghai University, Shanghai 200444, China

Received  January 2012 Revised  May 2012 Published  February 2013

The purpose of the paper is to develop globally convergent algorithms for solving the popular stationarity systems for mathematical programs with complementarity constraints (MPCC) directly. Since the popular stationarity systems for MPCC contain some unknown index sets, we first present some nonsmooth reformulations for the stationarity systems by removing the unknown index sets and then we propose a Levenberg-Marquardt type method to solve them. Under some regularity conditions, we show that the proposed method is globally and superlinearly convergent. We further report some preliminary numerical results.
Citation: Lei Guo, Gui-Hua Lin. Globally convergent algorithm for solving stationary points for mathematical programs with complementarity constraints via nonsmooth reformulations. Journal of Industrial & Management Optimization, 2013, 9 (2) : 305-322. doi: 10.3934/jimo.2013.9.305
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show all references

References:
[1]

$2^{nd}$ edition, Athena Scientific, Belmont, Massachusetts, 1999. Google Scholar

[2]

SIAM J. Optim., 7 (1997), 225-247. doi: 10.1137/S1052623494279110.  Google Scholar

[3]

Optim., 24 (1992), 269-284. doi: 10.1080/02331939208843795.  Google Scholar

[4]

J. Optim. Theory Appl., 124 (2005), 595-614. doi: 10.1007/s10957-004-1176-x.  Google Scholar

[5]

SIAM J. Optim., 17 (2006), 259-286. doi: 10.1137/S1052623402407382.  Google Scholar

[6]

Proceedings of the ICKS'04, IEEE Computer Society, (2004), 206-213. Google Scholar

[7]

J. Optim. Theory Appl., (2012). doi: 10.1007/s10957-012-0084-8.  Google Scholar

[8]

S. Leyffer, MacMPEC-ampl collection of mathematical programms with equilibrium constraints. Available from:, , ().   Google Scholar

[9]

G.-H. Lin, L. Guo and J.-J. Ye, Solving mathematical programs with equilibrium constraints as constrained equations,, preprint., ().   Google Scholar

[10]

Math. Program., 75 (1996), 407-439. doi: 10.1016/S0025-5610(96)00028-7.  Google Scholar

[11]

Cambridge University Press, Cambridge, 1996. doi: 10.1017/CBO9780511983658.  Google Scholar

[12]

Nonconvex Optimization and its Applications, 28, Kluwer Academic Publishers, Dordrecht, 1998.  Google Scholar

[13]

Math. Program., 51 (1991), 101-131. doi: 10.1007/BF01586928.  Google Scholar

[14]

Math. Program., 60 (1993), 295-337. doi: 10.1007/BF01580617.  Google Scholar

[15]

SIAM J. Optim., 3 (1993), 443-465. doi: 10.1137/0803021.  Google Scholar

[16]

Math. Program., 58 (1993), 353-367. doi: 10.1007/BF01581275.  Google Scholar

[17]

J. Optim. Theory Appl., 89 (1996), 17-37. doi: 10.1007/BF02192639.  Google Scholar

[18]

J. Math. Anal. Appl., 307 (2005), 350-369. doi: 10.1016/j.jmaa.2004.10.032.  Google Scholar

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