Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 162, Issue 1, Pages 208-248Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-013-0426-1
Keywords
Optimal control; Deterministic global optimization; Spatial branch-and-bound
Funding
- Engineering and Physical Sciences Research Council (EPSRC) [EP/J006572/1]
- Centre of Process Systems Engineering (CPSE) of Imperial College
- EPSRC [EP/J006572/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/J006572/1] Funding Source: researchfish
Ask authors/readers for more resources
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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available