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Nonsmooth Extended Cutting Plane Method for Generally Convex MINLP Problems

Ville-Pekka Eronen, Marko M. Mäkelä, Tapio Westerlund, Nonsmooth Extended Cutting Plane Method for Generally Convex MINLP Problems. TUCS Technical Reports 1055, TUCS, 2012.

Abstract:

In this article a generalization of the $\alpha$ECP algorithm to cover nondifferentiable Mixed-Integer NonLinear Programming (MINLP) problems is studied. In the generalization constraint functions are required to be $f^{\circ}$-pseudoconvex instead of pseudoconvex functions. This enables the functions to be nonsmooth. The objective function is first assumed to be linear but also $f^\circ$-pseudoconvex case is considered. Furthermore, the gradients used in the $\alpha$ECP algorithm are replaced by the subgradients of Clarke subdifferential. With some additional assumptions the resulting algorithm shall be proven to converge to a global minimum.

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BibTeX entry:

@TECHREPORT{tErMxWe12a,
  title = {Nonsmooth Extended Cutting Plane Method for Generally Convex MINLP Problems},
  author = {Eronen, Ville-Pekka and Mäkelä, Marko M. and Westerlund, Tapio},
  number = {1055},
  series = {TUCS Technical Reports},
  publisher = {TUCS},
  year = {2012},
  keywords = {Nonsmooth MINLP; Mixed-integer programming; Nonsmooth optimization; Extended cutting plane algorithm;  $\alpha$ECP; Subgradient; Pseudoconvex function; Generalized convexity},
  ISBN = {978-952-12-2769-1},
}

Belongs to TUCS Research Unit(s): Turku Optimization Group (TOpGroup)

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