Lifting mathematical programs with complementarity constraints

  • Authors:

  • Oliver Stein

  • Affiliations:

  • Karlsruhe Institute of Technology, Institute of Operations Research, Karlsruhe, Germany

  • Venue:
  • Mathematical Programming: Series A and B
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

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.