research-article

On branching rules for convex mixed-integer nonlinear optimization

Authors:

Andreas WächterAuthors Info & Claims

Journal of Experimental Algorithmics (JEA), Volume 18

Article No.: 2.6, Pages 2.1 - 2.31

https://doi.org/10.1145/2532568

Published: 28 November 2013 Publication History

Abstract

Branch-and-Bound (B&B) is perhaps the most fundamental algorithm for the global solution of convex Mixed-Integer Nonlinear Programming (MINLP) problems. It is well-known that carrying out branching in a nonsimplistic manner can greatly enhance the practicality of B&B in the context of Mixed-Integer Linear Programming (MILP). No detailed study of branching has heretofore been carried out for MINLP. In this article, we study and identify useful sophisticated branching methods for MINLP, including novel approaches based on approximations of the nonlinear relaxations by linear and quadratic programs.

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Mahajan ALeyffer SLinderoth JLuedtke JMunson T(2020)Minotaur: a mixed-integer nonlinear optimization toolkitMathematical Programming Computation10.1007/s12532-020-00196-1Online publication date: 7-Nov-2020
https://doi.org/10.1007/s12532-020-00196-1
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Published In

cover image ACM Journal of Experimental Algorithmics

ACM Journal of Experimental Algorithmics Volume 18, Issue

2013

329 pages

ISSN:1084-6654

EISSN:1084-6654

DOI:10.1145/2444016

Issue’s Table of Contents

Copyright © 2013 Public Domain.

This paper is authored by an employee(s) of the United States Government and is in the public domain. Non-exclusive copying or redistribution is allowed, provided that the article citation is given and the authors and agency are clearly identified as its source.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 November 2013

Accepted: 01 September 2013

Revised: 01 June 2013

Received: 01 October 2012

Published in JEA Volume 18

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Cited By

Liao J(2023)Optimizing Privacy-Preserving Content-Centric NetworksICC 2023 - IEEE International Conference on Communications10.1109/ICC45041.2023.10279248(4360-4365)Online publication date: 28-May-2023
https://doi.org/10.1109/ICC45041.2023.10279248
Mahajan ALeyffer SLinderoth JLuedtke JMunson T(2020)Minotaur: a mixed-integer nonlinear optimization toolkitMathematical Programming Computation10.1007/s12532-020-00196-1Online publication date: 7-Nov-2020
https://doi.org/10.1007/s12532-020-00196-1
Hakobyan AKim GYang I(2019)Risk-Aware Motion Planning and Control Using CVaR-Constrained OptimizationIEEE Robotics and Automation Letters10.1109/LRA.2019.29299804:4(3924-3931)Online publication date: Oct-2019
https://doi.org/10.1109/LRA.2019.2929980
Lubin MYamangil EBent RVielma J(2018)Polyhedral approximation in mixed-integer convex optimizationMathematical Programming: Series A and B10.5555/3288898.3288934172:1-2(139-168)Online publication date: 1-Nov-2018
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Lubin MYamangil EBent RVielma J(2017)Polyhedral approximation in mixed-integer convex optimizationMathematical Programming10.1007/s10107-017-1191-y172:1-2(139-168)Online publication date: 14-Sep-2017
https://doi.org/10.1007/s10107-017-1191-y
Costa MRocha AFrancisco RFernandes E(2016)Firefly penalty-based algorithm for bound constrained mixed-integer nonlinear programmingOptimization10.1080/02331934.2015.113592065:5(1085-1104)Online publication date: 27-Jan-2016
https://doi.org/10.1080/02331934.2015.1135920
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