An algorithmic framework for convex mixed integer nonlinear programs
Pierre Bonami,Lorenz T. Biegler,Andrew R. Conn,Gérard Cornuéjols,Ignacio E. Grossmann,Carl D. Laird,Jon Lee,Andrea Lodi,François Margot,Nicolas Sawaya,Andreas Wächter +10 more
TLDR
A class of hybrid algorithms, of which branch-and-bound and polyhedral outer approximation are the two extreme cases, are proposed and implemented and Computational results that demonstrate the effectiveness of this framework are reported.About:
This article is published in Discrete Optimization.The article was published on 2008-05-01 and is currently open access. It has received 891 citations till now. The article focuses on the topics: Branch and price & Integer programming.read more
Citations
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Journal ArticleDOI
Branching and bounds tighteningtechniques for non-convex MINLP
TL;DR: An sBB software package named couenne (Convex Over- and Under-ENvelopes for Non-linear Estimation) is developed and used for extensive tests on several combinations of BT and branching techniques on a set of publicly available and real-world MINLP instances and is compared with a state-of-the-art MINLP solver.
Journal ArticleDOI
Mixed-integer nonlinear optimization
TL;DR: An emerging area of mixed-integer optimal control that adds systems of ordinary differential equations to MINLP is described and a range of approaches for tackling this challenging class of problems are discussed, including piecewise linear approximations, generic strategies for obtaining convex relaxations for non-convex functions, spatial branch-and-bound methods, and a small sample of techniques that exploit particular types of non- Convex structures to obtain improved convex Relaxations.
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Non-convex mixed-integer nonlinear programming: A survey
Samuel Burer,Adam N. Letchford +1 more
TL;DR: In this paper, the authors survey the literature on non-convex mixed-integer nonlinear programs, discussing applications, algorithms, and software, and special attention is paid to the case in which the objective and constraint functions are quadratic.
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ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations
TL;DR: The purpose of this paper is to show how the extensible structure of ANTIGONE realizes the authors' previously-proposed mixed- integer quadratically-constrained quadratic program and mixed-integer signomial optimization computational frameworks.
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Scope for industrial applications of production scheduling models and solution methods
Iiro Harjunkoski,Christos T. Maravelias,Peter Bongers,Pedro M. Castro,Sebastian Engell,Ignacio E. Grossmann,John N. Hooker,Carlos A. Méndez,Guido Sand,John M. Wassick +9 more
TL;DR: The aim of the paper is to focus on the industrial aspects of scheduling and discuss the main characteristics, including strengths and weaknesses of the presented approaches, as well as some lessons learned from industry.
References
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On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
TL;DR: A comprehensive description of the primal-dual interior-point algorithm with a filter line-search method for nonlinear programming is provided, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix.
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Generalized Benders decomposition
TL;DR: In this paper, the extremal value of the linear program as a function of the parameterizing vector and the set of values of the parametric vector for which the program is feasible were derived using linear programming duality theory.
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An outer-approximation algorithm for a class of mixed-integer nonlinear programs
TL;DR: An outer-approximation algorithm is presented for solving mixed-integer nonlinear programming problems of a particular class and a theoretical comparison with generalized Benders decomposition is presented on the lower bounds predicted by the relaxed master programs.