Method for solving generalized convex nonsmooth mixed-integer nonlinear programming problems

Ville-Pekka Eronen, Jan Kronqvist, Tapio Westerlund, Marko M. Mäkelä, Napsu Karmitsa

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)


In this paper, we generalize the extended supporting hyperplane algorithm for a convex continuously differentiable mixed-integer nonlinear programming problem to solve a wider class of nonsmooth problems. The generalization is made by using the subgradients of the Clarke subdifferential instead of gradients. Consequently, all the functions in the problems are assumed to be locally Lipschitz continuous. The algorithm is shown to converge to a global minimum of an MINLP problem if the objective function is convex and the constraint functions are f∘-pseudoconvex. With some additional assumptions, the constraint functions may be f∘-quasiconvex.
Original languageUndefined/Unknown
Pages (from-to)443–459
Number of pages17
JournalJournal of Global Optimization
Issue number2
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed


  • Extended supporting hyperplane method
  • Convex optimization
  • Clarke subdifferential
  • Generalized convexities
  • nonsmooth optimization

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