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research
Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control
Authors
A. Bompadre
A. Flores Tlacuahuac
+70 more
A. Mitsos
A. Mitsos
A. Neumaier
A.B. Kurzhanski
A.B. Kurzhanski
A.B. Singer
A.B. Singer
A.E. Bryson
A.F. Filippov
A.M. Sahlodin
A.M. Sahlodin
B. Bhattacharjee
B. Chachuat
B. Chachuat
B. Houska
B. Houska
B. Houska
Benoît Chachuat
Boris Houska
C.A. Floudas
C.P. Neuman
C.S. Adjiman
D. Gottlieb
D.B. Leineweber
E.B. Saff
E.F. Galperin
G. Verfaillie
G.P. McCormick
H.G. Bock
I. Papamichail
J. Björnberg
J.A. Egea
J.B. Lasserre
J.K. Scott
J.K. Scott
J.K. Scott
J.R. Banga
J.T. Betts
K.L. Teo
L. Ruan
L.S. Pontryagin
L.T. Biegler
M. Berz
M. Neher
M. Tawarmalani
N.S. Nedialkov
N.V.B. Sahinidis
O. Stryk von
P. Agarwal
P. Belotti
R. Brusch
R. Horst
R. Horst
R. Luss
R. Luss
R.B. Kearfott
R.B. Kearfott
R.E. Bellman
R.W.H. Sargent
S. Boyd
S.J. Parulekar
T. Achterberg
T.H. Tsang
V. Azhmyakov
W. Walter
W.R. Esposito
W.R. Esposito
Y. Lin
Y. Lin
Y. Zhao
Publication date
1 January 2014
Publisher
'Springer Science and Business Media LLC'
Doi
Cite
Abstract
This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York
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Last time updated on 17/02/2017
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info:doi/10.1007%2Fs10957-013-...
Last time updated on 11/12/2019