Alternative regularizations for Outer-Approximation algorithms for convex MINLP

David E. Bernal, Zedong Peng, Jan Kronqvist and Ignacio E. Grossmann ()
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David E. Bernal: NASA Ames Research Center
Zedong Peng: Zhejiang University
Jan Kronqvist: KTH Royal Institute of Technology
Ignacio E. Grossmann: Carnegie Mellon University

Journal of Global Optimization, 2022, vol. 84, issue 4, No 1, 807-842

Abstract: Abstract In this work, we extend the regularization framework from Kronqvist et al. (Math Program 180(1):285–310, 2020) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance metrics and Lagrangean approximations, used in the projection problem for finding new integer combinations to be used within the Outer-Approximation (OA) method. The new approach, called Regularized Outer-Approximation (ROA), has been implemented as part of the open-source Mixed-integer nonlinear decomposition toolbox for Pyomo—MindtPy. We compare the OA method with seven regularization function alternatives for ROA. Moreover, we extend the LP/NLP Branch and Bound method proposed by Quesada and Grossmann (Comput Chem Eng 16(10–11):937–947, 1992) to include regularization in an algorithm denoted RLP/NLP. We provide convergence guarantees for both ROA and RLP/NLP. Finally, we perform an extensive computational experiment considering all convex MINLP problems in the benchmark library MINLPLib. The computational results show clear advantages of using regularization combined with the OA method.

Keywords: Convex MINLP; Outer-Approximation; Regularization for mixed-integer optimization (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-022-01178-4

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