On the generalization of ECP and OA methods to nonsmooth convex MINLP problems

In this article, generalization of some mixed-integer nonlinear programming algorithms to cover convex nonsmooth problems is studied. In the extended cutting plane method, gradients are replaced by the subgradients of the convex function and the resulting algorithm shall be proved to converge to a g...

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Vydané v:Optimization Ročník 63; číslo 7; s. 1057 - 1073
Hlavní autori: Eronen, Ville-Pekka, Mäkelä, Marko M., Westerlund, Tapio
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia Taylor & Francis Group 01.07.2014
Taylor & Francis LLC
Predmet:
Algorithms
Approximation
Cutting
extended cutting plane algorithm
Integer programming
Mathematical analysis
Mathematical functions
Mathematical models
Mathematical problems
Nonlinear programming
nonsmooth optimization
Numerical analysis
Optimization
Optimization algorithms
outer approximation algorithm
Planes
Studies
subgradient
ISSN:0233-1934, 1029-4945
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Shrnutí:In this article, generalization of some mixed-integer nonlinear programming algorithms to cover convex nonsmooth problems is studied. In the extended cutting plane method, gradients are replaced by the subgradients of the convex function and the resulting algorithm shall be proved to converge to a global optimum. It is shown through a counterexample that this type of generalization is insufficient with certain versions of the outer approximation algorithm. However, with some modifications to the outer approximation method a special type of nonsmooth functions for which the subdifferential at any point is a convex combination of a finite number of subgradients at the point can be considered. Numerical results with extended cutting plane method are also reported.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2012.712118