Ignacio Grossmann: Alternative Regularizations for Outer-Approximation Algorithms for Convex MINLP скачать в хорошем качестве

Ignacio Grossmann: Alternative Regularizations for Outer-Approximation Algorithms for Convex MINLP

Authors: David E. Bernal, Carnegie Mellon University, Pittsburgh Zedong Peng, Zhejiang University, Hangzhou Jan Kronqvist, Imperial College, London Ignacio E. Grossmann, Carnegie Mellon University, Pittsburgh In this work, we extend the regularization framework from Kronqvist et al. [1] 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 (2). 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 & Bound method proposed by Quesada and Grossmann [3] 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 experiments by considering all convex MINLP problems in the benchmark library MINLPLib. The computational results show clear advantages of using regularization in combination with the OA method. [1] Kronqvist, J., D.E. Bernal, I.E. Grossmann, “Using Regularization and Second Order Information in Outer Approximation for Convex MINLP” Mathematical Programming, 180:285–310 (2020). [2] Duran, M.A. and I.E. Grossmann, "An Outer-Approximation Algorithm for a Class of Mixed-integer Nonlinear Programs," Math Programming 36, 307 (1986). [3] Quesada, I. and I.E. Grossmann, "An LP/NLP Based Branch and Bound Algorithm for MINLP Optimization," Computers and Chemical Engineering, 16, 937 (1992). ~ This talk was submitted to MINLP Virtual Workshop 2021 (https://optimisation.doc.ic.ac.uk/min...) Connect with the Computational Optimisation Group at Imperial College London online... Subscribe to the CogImperial YouTube channel for more research related content:    / @cogimperial   Follow us on Twitter for news about our research group:   / cogimperial   Visit our official site for more information: https://optimisation.doc.ic.ac.uk/