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Hidden invariant convexity for global and conic-intersection optimality guarantees in discrete-time optimal control

Author

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  • Jorn H. Baayen

    (KISTERS Group, Business Unit Water
    University of Amsterdam)

  • Krzysztof Postek

    (Delft University of Technology)

Abstract

Non-convex discrete-time optimal control problems in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and numerical experience indicates that algorithms aiming for Karush–Kuhn–Tucker points often find solutions that are indistinguishable from global optima. In our paper, we provide a theoretical underpinning for this phenomenon, showing that on a broad class of problems the objective can be shown to be an invariant convex function (invex function) of the control decision variables when state variables are eliminated using implicit function theory. In this way, optimality guarantees can be obtained, the exact nature of which depends on the position of the solution within the feasible set. In a numerical example, we show how high-quality solutions are obtained with local search for a river control problem where invexity holds.

Suggested Citation

  • Jorn H. Baayen & Krzysztof Postek, 2022. "Hidden invariant convexity for global and conic-intersection optimality guarantees in discrete-time optimal control," Journal of Global Optimization, Springer, vol. 82(2), pages 263-281, February.
    • Handle: RePEc:spr:jglopt:v:82:y:2022:i:2:d:10.1007_s10898-021-01072-5
    DOI: 10.1007/s10898-021-01072-5
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    References listed on IDEAS

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    1. Ghaddar, Bissan & Claeys, Mathieu & Mevissen, Martin & Eck, Bradley J., 2017. "Polynomial optimization for water networks: Global solutions for the valve setting problem," European Journal of Operational Research, Elsevier, vol. 261(2), pages 450-459.
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