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On Convex Nonsmooth MINLP

Ville-Pekka Eronen, Marko M. Mäkelä, Tapio Westerlund, On Convex Nonsmooth MINLP. TUCS Technical Reports 988, Turku Centre for Computer Science, 2010.

Abstract:

In this article generalization of some MINLP 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 proven 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 OA 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.

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BibTeX entry:

@TECHREPORT{tErMaWe10a,
  title = {On Convex Nonsmooth MINLP},
  author = {Eronen, Ville-Pekka and Mäkelä, Marko M. and Westerlund, Tapio},
  number = {988},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2010},
  keywords = {Convex nonsmooth MINLP; Convex programming; Extended cutting plane algorithm; MINLP; Nonsmooth optimization; Outer approximation algorithm; Subgradient},
  ISBN = {978-952-12-2495-9},
}

Belongs to TUCS Research Unit(s): Other

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