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Extended Supporting Hyperplane Algorithm for Generalized Convex Nonsmooth MINLP Problems

Ville-Pekka Eronen, Jan Kronqvist, Tapio Westerlund, Marko M. Mäkelä, Napsu Karmitsa, Extended Supporting Hyperplane Algorithm for Generalized Convex Nonsmooth MINLP Problems. TUCS Technical Reports 1179, TUCS, 2017.

Abstract:

In this paper the extended supporting hyperplane algorithm is generalized for a class of nonsmooth mixed-integer nonlinear programming problems. The generalization is to use the subgradients of the Clarke subdifferential instead of gradients. Consequently, all the functions in the problem are assumed to be locally Lipschitz continuous. The algorithm is shown to converge to a global minimizer of the problem if the objective function is convex and the constraint functions are f0-pseudoconvex. Some numerical experiments are done on the parameters of the algorithm. In addition, ESH is compared against alphaECP.

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BibTeX entry:

@TECHREPORT{tErKrWeMxKa17a,
  title = {Extended Supporting Hyperplane Algorithm for Generalized Convex Nonsmooth MINLP Problems},
  author = {Eronen, Ville-Pekka and Kronqvist, Jan and Westerlund, Tapio and Mäkelä, Marko M. and Karmitsa, Napsu},
  number = {1179},
  series = {TUCS Technical Reports},
  publisher = {TUCS},
  year = {2017},
  keywords = {ESH; Nonsmooth MINLP; Convex optimization; Generalized convexity; Clarke generalized derivatives;},
}

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

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