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

A1 Originalartikel i en vetenskaplig tidskrift (referentgranskad)

Interna författare/redaktörer

Publikationens författare: Ville-Pekka Eronen, Jan Kronqvist, Tapio Westerlund, Marko M. Mäkelä, Napsu Karmitsa
Förläggare: SPRINGER
Publiceringsår: 2017
Tidskrift: Journal of Global Optimization
Tidskriftsakronym: J GLOBAL OPTIM
Volym: 69
Nummer: 2
Artikelns första sida, sidnummer: 443
Artikelns sista sida, sidnummer: 459
Antal sidor: 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

Senast uppdaterad 2019-13-12 vid 04:35