Lifting mathematical programs with complementarity constraints

• 成果类型: Article
• 署名作者: Stein, Oliver
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-010-0345-y
• 发表日期: 2012
• 页码: 71-94
• 关键词: search filter methods; elastic-mode; CONVERGENCE; point; Penalization; set; regularization; stationarity; algorithms; STABILITY

摘要

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.