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

Ville-Pekka Eronen (), Jan Kronqvist, Tapio Westerlund, Marko M. Mäkelä and Napsu Karmitsa
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Ville-Pekka Eronen: University of Turku
Jan Kronqvist: Åbo Akademi
Tapio Westerlund: Åbo Akademi
Marko M. Mäkelä: University of Turku
Napsu Karmitsa: University of Turku

Journal of Global Optimization, 2017, vol. 69, issue 2, No 7, 443-459

Abstract: Abstract 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 $$f^{\circ }$$ f ∘ -pseudoconvex. With some additional assumptions, the constraint functions may be $$f^{\circ }$$ f ∘ -quasiconvex.

Keywords: MINLP; Extended supporting hyperplane method; Convex optimization; Nonsmooth optimization; Clarke subdifferential; Generalized convexities; 90C11; 90C25 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-017-0528-7

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