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

    7 Citations (Scopus)

    Abstract

    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
    Volume69
    Issue number2
    DOIs
    Publication statusPublished - 2017
    MoE publication typeA1 Journal article-refereed

    Keywords

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

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