A1 Refereed original research article in a scientific journal
Method for solving generalized convex nonsmooth mixed-integer nonlinear programming problems
Authors: Eronen VP, Kronqvist J, Westerlund T, Mäkelä MM, Karmitsa N
Publisher: SPRINGER
Publishing place: 000410819100007
Publication year: 2017
Journal: Journal of Global Optimization
Journal name in source: JOURNAL OF GLOBAL OPTIMIZATION
Journal acronym: J GLOBAL OPTIM
Volume: 69
Issue: 2
First page : 443
Last page: 459
Number of pages: 17
ISSN: 0925-5001
eISSN: 1573-2916
DOI: https://doi.org/10.1007/s10898-017-0528-7
Web address : 10.1007/s10898-017-0528-7
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/26899604
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 degrees-pseudoconvex. With some additional assumptions, the constraint functions may be f degrees-quasiconvex.
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