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

A1 Journal article (refereed)

Internal Authors/Editors

Publication Details

List of Authors: Ville-Pekka Eronen, Jan Kronqvist, Tapio Westerlund, Marko M. Mäkelä, Napsu Karmitsa
Publisher: SPRINGER
Publication year: 2017
Journal: Journal of Global Optimization
Journal acronym: J GLOBAL OPTIM
Volume number: 69
Issue number: 2
Start page: 443
End page: 459
Number of pages: 17
ISSN: 0925-5001
eISSN: 1573-2916


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.


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

Last updated on 2019-16-10 at 03:15