Lifting mathematical programs with complementarity constraints
- First Online:
- 396 Downloads
We present a new smoothing approach for mathematical programs with complementarity constraints, based on the orthogonal projection of a smooth manifold. We study regularity of the lifted feasible set and, since the corresponding optimality conditions are inherently degenerate, introduce a regularization approach involving a novel concept of tilting stability. A correspondence between the C-index in the original problem and the quadratic index in the lifted problem is shown. In particular, a local minimizer of the mathematical program with complementarity constraints may numerically be found by minimization of the lifted, smooth problem. We report preliminary computational experience with the lifting approach.
KeywordsRegularization Smoothing Lifting Numerical method
Mathematics Subject Classification (2000)90C33 90C46
Unable to display preview. Download preview PDF.
- 4.Bouza Allende, G.: Mathematical programs with equilibrium constraints: solution techniques from parametric optimization, Ph.D. thesis, University of Twente (2006)Google Scholar
- 8.Fukushima M., Pang J.: Convergence of a smoothing continuation method for mathematical programs with complementarity constraints. In: Théra, M., Tichatschke, R. (eds) Ill-posed Variational Problems and Regularization Techniques. Lecture Notes in Economics and Mathematical Systems, vol. 447, pp. 99–110, pp. 99–110. Springer, Heidelberg (1999)Google Scholar
- 21.Leyffer, S.: MacMPEC—ampl collection of Mathematical Programs with Equilibrium Constraints. http://wiki.mcs.anl.gov/leyffer/index.php/MacMPEC (2009)
- 25.Luo Z.-Q., Pang J.S., Ralph D.: Piecewise sequential quadratic programming for mathematical programs with nonlinear complementarity constraints. In: Migdalas, A., Pardalos, P., Värbrand, P. (eds) Multilevel Optimization: Algorithms, Complexity, and Applications, pp. 209–229. Kluwer Academic Publishers, Dordrecht (1998)CrossRefGoogle Scholar
- 29.Ralph, D., Stein, O.: Homotopy methods for quadratic programs with complementarity constraints. Preprint No. 120, Department of Mathematics - C, RWTH Aachen University (2006)Google Scholar
- 34.Stöhr M.: Nonsmooth trust region methods and their applications to mathematical programs with equilibrium constraints. Shaker-Verlag, Aachen (1999)Google Scholar