TY - JOUR
T1 - Method for solving generalized convex nonsmooth mixed-integer nonlinear programming problems
AU - Eronen, Ville-Pekka
AU - Kronqvist, Jan
AU - Westerlund, Tapio
AU - Mäkelä, Marko M.
AU - Karmitsa, Napsu
N1 - ast.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
KW - Extended supporting hyperplane method
KW - Convex optimization
KW - Clarke subdifferential
KW - Generalized convexities
KW - MINLP
KW - nonsmooth optimization
KW - Extended supporting hyperplane method
KW - Convex optimization
KW - Clarke subdifferential
KW - Generalized convexities
KW - MINLP
KW - nonsmooth optimization
KW - Extended supporting hyperplane method
KW - Convex optimization
KW - Clarke subdifferential
KW - Generalized convexities
KW - MINLP
KW - nonsmooth optimization
U2 - 10.1007/s10898-017-0528-7
DO - 10.1007/s10898-017-0528-7
M3 - Artikel
SN - 0925-5001
VL - 69
SP - 443
EP - 459
JO - Journal of Global Optimization
JF - Journal of Global Optimization
IS - 2
ER -