Linearization-based algorithms for mixed-integer nonlinear programs with convex continuous relaxation

We present two linearization-based algorithms for mixed-integer nonlinear programs (MINLPs) having a convex continuous relaxation. The key feature of these algorithms is that, in contrast to most existing linearization-based algorithms for convex MINLPs, they do not require the continuous relaxation...

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Bibliographic Details
Published in:Journal of global optimization Vol. 59; no. 2-3; pp. 343 - 365
Main Authors: Hamzeei, Mahdi, Luedtke, James
Format: Journal Article
Language:English
Published: Boston Springer US 01.07.2014
Springer
Springer Nature B.V
Subjects:
Algorithms
Approximation
Computation
Computer Science
Convex analysis
Integer programming
Linear programming
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Nonlinear programming
Nonlinearity
Operations Research/Decision Theory
Optimization
Real Functions
Studies
Texts
Mixed-integer nonlinear programming
Quasiconvex function
Outer approximation
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:We present two linearization-based algorithms for mixed-integer nonlinear programs (MINLPs) having a convex continuous relaxation. The key feature of these algorithms is that, in contrast to most existing linearization-based algorithms for convex MINLPs, they do not require the continuous relaxation to be defined by convex nonlinear functions. For example, these algorithms can solve to global optimality MINLPs with constraints defined by quasiconvex functions. The first algorithm is a slightly modified version of the LP/NLP-based branch-and-bouund ( LP/NLP-BB ) algorithm of Quesada and Grossmann, and is closely related to an algorithm recently proposed by Bonami et al. (Math Program 119:331–352, 2009 ). The second algorithm is a hybrid between this algorithm and nonlinear programming based branch-and-bound. Computational experiments indicate that the modified LP/NLP-BB method has comparable performance to LP/NLP-BB on instances defined by convex functions. Thus, this algorithm has the potential to solve a wider class of MINLP instances without sacrificing performance.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-014-0172-4