MPCC Strategies for Nonsmooth NLPs

This paper develops solution strategies for large-scale nonsmooth optimization problems. We transform nonsmooth programs into equivalent mathematical programs with complementarity constraints (MPCCs), and then employ NLP-based strategies for their so- lution. For this purpose, two NLP formulations based on complementarity relaxations are put forward, one of which applies a parameterized formulation and operates with a bound- ing algorithm, with the aim of taking advantage of the NLP sensitivities in search for the solution; and the other relates closely to the well-studied Lin-Fukushima formulation. With appropriate assumptions, the resulting solution of the proposed formulations is proved to be C- and M-stationary for the MPCC problems. Numerical performance of the proposed formulations, and the formulations by Lin & Fukushima and Scholtes are studied and com- pared, with selected examples from the MacMPEC collection and two large-scale distillation cases.


CAPD Report B-26-21, Center for Advanced Process Decision-Making, Carnegie Mellon University, 10/21



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