Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control

  • Boris Houska
  • Benoît Chachuat


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.


Optimal control Deterministic global optimization Spatial branch-and-bound 



This paper is based upon work supported by the Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/J006572/1. Financial support from the Centre of Process Systems Engineering (CPSE) of Imperial College is gratefully acknowledged. The authors are grateful to the reviewers for the thoughtful comments that led to substantial improvement of the article.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Centre for Process Systems Engineering, Department of Chemical EngineeringImperial College LondonLondonUK

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