Extended cutting plane method for a class of nonsmooth nonconvex MINLP problems

Ville-Pekka Eronen, Marko M. Mäkelä, Tapio Westerlund

    Research output: Contribution to journalArticleScientificpeer-review

    10 Citations (Scopus)

    Abstract

    In this article, a generalization of the ECP algorithm to cover a class of nondifferentiable Mixed-Integer NonLinear Programming problems is studied. In the generalization constraint functions are required to be -pseudoconvex instead of pseudoconvex functions. This enables the functions to be nonsmooth. The objective function is first assumed to be linear but also -pseudoconvex case is considered. Furthermore, the gradients used in the 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.
    Original languageUndefined/Unknown
    Pages (from-to)641–661
    Number of pages21
    JournalOptimization
    Volume64
    Issue number3
    DOIs
    Publication statusPublished - 2015
    MoE publication typeA1 Journal article-refereed

    Keywords

    • alpha ECP
    • extended cutting plane algorithm
    • generalized convexity
    • mixed-integer programming
    • nonsmooth MINLP
    • nonsmooth optimization
    • pseudoconvex function
    • subgradient

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