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MPCC strategies for nonsmooth nonlinear programs

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Abstract

This paper develops solution strategies for large-scale nonsmooth optimization problems. We transform nonsmooth programs into equivalent mathematical programs with complementarity constraints (MPCCs), and devise NLP-based strategies for their solution. For this purpose, two NLP formulations based on complementarity relaxations are put forward, one of which applies a parameterized formulation and operates with a bounding 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. Relations between the solutions of these NLPs and of the MPCC is revealed by sensitivity analysis. With appropriate assumptions, the resulting solution of the NLP formulations are proved to be C- and M-stationary for the MPCCs in the limit. Numerical performance of the proposed formulations, and the formulations by Lin & Fukushima and by Scholtes are studied and compared, with selected examples from the MacMPEC collection and two large-scale distillation cases.

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Acknowledgements

Support for this study was provided from an unrestricted grant from Carrier Corporation, and is gratefully acknowledged. We are also grateful to Dr. Alexandra Schwartz for her great help in MacMPEC/MATLAB interface, and to Dr. Helena Sofia Rodrigues and Dr. M. Teresa T. Monteiro for their kind help in AMPL/MATLAB interface.

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Authors and Affiliations

  1. College of Control Science and Engineering, Zhejiang University, Hangzhou, Zhejiang, 310027, China

    K. Wang

  2. Chemical Engineering Department, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    L. T. Biegler

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  1. K. Wang
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  2. L. T. Biegler
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Correspondence to L. T. Biegler.

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Wang, K., Biegler, L.T. MPCC strategies for nonsmooth nonlinear programs. Optim Eng 24, 1883–1929 (2023). https://doi.org/10.1007/s11081-022-09755-y

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