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Lifting mathematical programs with complementarity constraints

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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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  1. Institute of Operations Research, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Oliver Stein

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  1. Oliver Stein
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Correspondence to Oliver Stein.

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Stein, O. Lifting mathematical programs with complementarity constraints. Math. Program. 131, 71–94 (2012). https://doi.org/10.1007/s10107-010-0345-y

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