Lifting mathematical programs with complementarity constraints |
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Authors: | Oliver Stein |
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Institution: | 1. Institute of Operations Research, Karlsruhe Institute of Technology, Karlsruhe, Germany
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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. |
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