Abstract
We study the behavior of a sequence generated by a smoothing continuation method for mathematical programs with equilibrium constraints (MPEC). In particular, we show that under the linear independence constraint qualification and an additional condition called the asymptotic weak nondegeneracy, the limit of KKT points satisfying the second-order necessary conditions for the perturbed problems is a B-stationary point of the original MPEC. The notable fact is that this result does not rely on the strict complementarity assumption at the limit point.
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References
Y. Chen and M. Florian, “The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions,” Optimization 32 (1995) 193–209.
F. Facchinei, H. Jiang and L. Qi, “A smoothing method for mathematical programs with equilibrium constraints,” Mathematical Programming, forthcoming.
A. Fischer, “A special Newton-type optimization method,” Optimization 24 (1992) 269–284.
M. Fukushima, Z.-Q. Luo and J.-S. Pang, “A globally convergent sequential programming algorithm for mathematical programs with linear complementarity constraints,” Computational Optimization and Applications 10 (1998) 5–30.
H. Jiang and D. Ralph, “Smooth SQP methods for mathematical programs with nonlinear complementarity constraints,” Working paper, Department of Mathematics and Statistics, University of Melbourne, Parkville, Australia, 1997.
C. Kanzow, “Some noninterior continuation methods for linear complementarity problems,” SIAM Journal on Matrix Analysis and Applications 17 (1996) 851–868.
Z.-Q. Luo, J.-S. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints, (Cambridge University Press, Cambridge, 1996).
J.V. Outrata, “Optimality conditions for a class of mathematical programs with equilibrium constraints,” Mathematics of Operations Research, forthcoming.
J. Outrata, M. Kočvara and J. Zowe, Nonsmooth Approach to Optimization Problems with Equilibrium Constraints, (Kluwer Academic Publishers, Dordrecht, 1998).
J. Outrata and J. Zowe, A numerical approach to optimization problems with variational inequality constraints, Mathematical Programming 68 (1995) 105–130.
J.-S. Pang and M. Fukushima, “Complementarity constraint qualifications and simplified B-stationarity conditions for mathematical programs with equilibrium constraints,” Computational Optimization and Applications, forthcoming.
H. Scheel and S. Scholtes, “Mathematical programs with equilibrium constraints: Stationarity, optimality, and sensitivity,” Working paper, The Judge Institute of Management Studies, University of Cambridge, Cambridge, 1997.
J.J. Ye, “Optimality conditions for optimization problems with complementarity constraints,” SIAM Journal on Optimization, forthcoming.
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© 1999 Springer-Verlag Berlin Heidelberg
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Fukushima, M., Pang, JS. (1999). Convergence of a Smoothing Continuation Method for Mathematical Progams with Complementarity Constraints. In: Théra, M., Tichatschke, R. (eds) Ill-posed Variational Problems and Regularization Techniques. Lecture Notes in Economics and Mathematical Systems, vol 477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45780-7_7
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DOI: https://doi.org/10.1007/978-3-642-45780-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66323-2
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