Alternative regularizations for Outer-Approximation algorithms for convex MINLP

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...

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Bibliographic Details
Published in:Journal of global optimization Vol. 84; no. 4; pp. 807 - 842
Main Authors: Bernal, David E., Peng, Zedong, Kronqvist, Jan, Grossmann, Ignacio E.
Format: Journal Article
Language:English
Published: Ames Research Center Springer 01.12.2022
Springer US
Springer Nature B.V
Subjects:
Algorithms
Approximation
Approximation algorithms
Branch and bound method
Branch and bound methods
Computer Programming And Software
Computer Science
Convex MINLP
Convex mixed-integer nonlinear programming
Integer programming
Mathematical analysis
Mathematics
Mathematics and Statistics
Mixed integer
Mixed integer non-linear programming problems
Mixed integer optimization
Mixed-integer nonlinear programming
Nonlinear programming
Open source software
Operations Research/Decision Theory
Optimization
Outer approximation
Outer approximation algorithm
Outer approximation methods
Real Functions
Regularisation
Regularization
Regularization for mixed-integer optimization
Regularization function
Trees (mathematics)
Outer Approximation
Convex Mixed-Integer Nonlinear Programming
Regularization
Mixed-Integer Optimization
Regularization for mixed-integer optimization
Outer-Approximation
Convex MINLP
ISSN:0925-5001, 1573-2916, 1573-2916
Online Access:Get full text
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Summary: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.
Bibliography:ARC
Ames Research Center
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ISSN:0925-5001
1573-2916
1573-2916
DOI:10.1007/s10898-022-01178-4