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

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

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    8 Citeringar (Scopus)

    Sammanfattning

    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.
    OriginalspråkOdefinierat/okänt
    Sidor (från-till)443–459
    Antal sidor17
    TidskriftJournal of Global Optimization
    Volym69
    Utgåva2
    DOI
    StatusPublicerad - 2017
    MoE-publikationstypA1 Tidskriftsartikel-refererad

    Nyckelord

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

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