Mathematical Programming

, Volume 131, Issue 1–2, pp 71–94 | Cite as

Lifting mathematical programs with complementarity constraints

Full Length Paper

Abstract

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.

Keywords

Regularization Smoothing Lifting Numerical method 

Mathematics Subject Classification (2000)

90C33 90C46 

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Copyright information

© Springer and Mathematical Programming Society 2010

Authors and Affiliations

  1. 1.Institute of Operations ResearchKarlsruhe Institute of TechnologyKarlsruheGermany

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