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An Alternating Trust Region Algorithm for Distributed Linearly Constrained Nonlinear Programs, Application to the Optimal Power Flow Problem

  • Jean-Hubert HoursEmail author
  • Colin N. Jones
Article

Abstract

A novel trust region method for solving linearly constrained nonlinear programs is presented. The proposed technique is amenable to a distributed implementation, as its salient ingredient is an alternating projected gradient sweep in place of the Cauchy point computation. It is proven that the algorithm yields a sequence that globally converges to a critical point. As a result of some changes to the standard trust region method, namely a proximal regularisation of the trust region subproblem, it is shown that the local convergence rate is linear with an arbitrarily small ratio. Thus, convergence is locally almost superlinear, under standard regularity assumptions. The proposed method is successfully applied to compute local solutions to alternating current optimal power flow problems in transmission and distribution networks. Moreover, the new mechanism for computing a Cauchy point compares favourably against the standard projected search, as for its activity detection properties.

Keywords

Nonconvex optimisation Distributed optimisation Coordinate gradient descent Trust region methods 

Mathematics Subject Classification

49M27 49M37 65K05 65K10 90C06 90C26 90C30 

Notes

Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2014)/ ERC Grant Agreement No. 307608.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Automatic Control LaboratoryEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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