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

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  • Jean-Hubert Hours

    (Ecole Polytechnique Fédérale de Lausanne)

  • Colin N. Jones

    (Ecole Polytechnique Fédérale de Lausanne)

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.

Suggested Citation

  • Jean-Hubert Hours & Colin N. Jones, 2017. "An Alternating Trust Region Algorithm for Distributed Linearly Constrained Nonlinear Programs, Application to the Optimal Power Flow Problem," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 844-877, June.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:3:d:10.1007_s10957-015-0853-2
    DOI: 10.1007/s10957-015-0853-2
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    References listed on IDEAS

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    1. Dan Xue & Wenyu Sun & Liqun Qi, 2014. "An alternating structured trust region algorithm for separable optimization problems with nonconvex constraints," Computational Optimization and Applications, Springer, vol. 57(2), pages 365-386, March.
    2. Quoc Tran Dinh & Carlo Savorgnan & Moritz Diehl, 2013. "Combining Lagrangian decomposition and excessive gap smoothing technique for solving large-scale separable convex optimization problems," Computational Optimization and Applications, Springer, vol. 55(1), pages 75-111, May.
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    Cited by:

    1. Salman Khodayifar & Mohammad A. Raayatpanah & Abbas Rabiee & Hamed Rahimian & Panos M. Pardalos, 2018. "Optimal Long-Term Distributed Generation Planning and Reconfiguration of Distribution Systems: An Accelerating Benders’ Decomposition Approach," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 283-310, October.

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