On the generalization of ECP and OA methods to nonsmooth convex MINLP problems

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

    Research output: Contribution to journalArticleScientificpeer-review

    18 Citations (Scopus)

    Abstract

    In this article, generalization of some mixed-integer nonlinear programming algorithms to cover convex nonsmooth problems is studied. In the extended cutting plane method, gradients are replaced by the subgradients of the convex function and the resulting algorithm shall be proved to converge to a global optimum. It is shown through a counterexample that this type of generalization is insufficient with certain versions of the outer approximation algorithm. However, with some modifications to the outer approximation method a special type of nonsmooth functions for which the subdifferential at any point is a convex combination of a finite number of subgradients at the point can be considered. Numerical results with extended cutting plane method are also reported.
    Original languageUndefined/Unknown
    Pages (from-to)1057–1073
    Number of pages17
    JournalOptimization
    Volume63
    Issue number7
    DOIs
    Publication statusPublished - 2014
    MoE publication typeA1 Journal article-refereed

    Keywords

    • extended cutting plane algorithm
    • nonsmooth optimization
    • outer approximation algorithm
    • subgradient

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