2020/02/24 by F. Harder, Harder, Felix, Patrick Mehlitz +3
Computer Science · Engineering · Mathematics · #49M05 #49M15 #90C30 #90C33 #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2002.10124
openalex publication_date 2020/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the Mordukhovich-stationarity system associated with a\nmathematical program with complementarity constraints (MPCC) can be\nequivalently written as a system of discontinuous equations which can be\ntackled with a semismooth Newton method. We show that the resulting algorithm\ncan be interpreted as an active set strategy for MPCCs. Local fast convergence\nof the method is guaranteed under validity of an MPCC-tailored version of LICQ\nand a suitable second-order condition. In case of linear-quadratic MPCCs, the\nLICQ-type constraint qualification can be replaced by a weaker condition which\ndepends on the underlying multipliers. We discuss a suitable globalization\nstrategy for our method. Some numerical results are presented in order to\nillustrate our theoretical findings.\n