IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v84y2023i1d10.1007_s10589-022-00386-8.html
   My bibliography  Save this article

An improved penalty algorithm using model order reduction for MIPDECO problems with partial observations

Author

Listed:
  • Dominik Garmatter

    (Department of Mathematics, Chemnitz University of Technology)

  • Margherita Porcelli

    (University of Bologna
    ISTI–CNR)

  • Francesco Rinaldi

    (University of Padova)

  • Martin Stoll

    (Department of Mathematics, Chemnitz University of Technology)

Abstract

This work addresses optimal control problems governed by a linear time-dependent partial differential equation (PDE) as well as integer constraints on the control. Moreover, partial observations are assumed in the objective function. The resulting problem poses several numerical challenges due to the mixture of combinatorial aspects, induced by integer variables, and large scale linear algebra issues, arising from the PDE discretization. Since classical solution approaches such as the branch-and-bound framework are typically overwhelmed by such large-scale problems, this work extends an improved penalty algorithm proposed by the authors, to the time-dependent setting. The main contribution is a novel combination of an interior point method, preconditioning, and model order reduction yielding a tailored local optimization solver at the heart of the overall solution procedure. A thorough numerical investigation is carried out both for the heat equation as well as a convection-diffusion problem demonstrating the versatility of the approach.

Suggested Citation

  • Dominik Garmatter & Margherita Porcelli & Francesco Rinaldi & Martin Stoll, 2023. "An improved penalty algorithm using model order reduction for MIPDECO problems with partial observations," Computational Optimization and Applications, Springer, vol. 84(1), pages 191-223, January.
    • Handle: RePEc:spr:coopap:v:84:y:2023:i:1:d:10.1007_s10589-022-00386-8
    DOI: 10.1007/s10589-022-00386-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-022-00386-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-022-00386-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Funke, S.W. & Farrell, P.E. & Piggott, M.D., 2014. "Tidal turbine array optimisation using the adjoint approach," Renewable Energy, Elsevier, vol. 63(C), pages 658-673.
    2. S. Bellavia, 1998. "Inexact Interior-Point Method," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 109-121, January.
    3. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    4. Markus Dihlmann & Bernard Haasdonk, 2015. "Certified PDE-constrained parameter optimization using reduced basis surrogate models for evolution problems," Computational Optimization and Applications, Springer, vol. 60(3), pages 753-787, April.
    5. S. Lucidi & F. Rinaldi, 2010. "Exact Penalty Functions for Nonlinear Integer Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 479-488, June.
    6. S. Göttlich & A. Potschka & C. Teuber, 2019. "A partial outer convexification approach to control transmission lines," Computational Optimization and Applications, Springer, vol. 72(2), pages 431-456, March.
    7. Sven Leyffer & Paul Manns & Malte Winckler, 2021. "Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation," Computational Optimization and Applications, Springer, vol. 79(1), pages 193-221, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stefania Bellavia & Valentina De Simone & Daniela di Serafino & Benedetta Morini, 2016. "On the update of constraint preconditioners for regularized KKT systems," Computational Optimization and Applications, Springer, vol. 65(2), pages 339-360, November.
    2. Gondzio, Jacek, 2016. "Crash start of interior point methods," European Journal of Operational Research, Elsevier, vol. 255(1), pages 308-314.
    3. Zhang, Yidan & Shek, Jonathan K.H. & Mueller, Markus A., 2023. "Controller design for a tidal turbine array, considering both power and loads aspects," Renewable Energy, Elsevier, vol. 216(C).
    4. du Feu, R.J. & Funke, S.W. & Kramer, S.C. & Hill, J. & Piggott, M.D., 2019. "The trade-off between tidal-turbine array yield and environmental impact: A habitat suitability modelling approach," Renewable Energy, Elsevier, vol. 143(C), pages 390-403.
    5. Castro, Jordi & Escudero, Laureano F. & Monge, Juan F., 2023. "On solving large-scale multistage stochastic optimization problems with a new specialized interior-point approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 268-285.
    6. Baheri, Ali & Ramaprabhu, Praveen & Vermillion, Christopher, 2018. "Iterative 3D layout optimization and parametric trade study for a reconfigurable ocean current turbine array using Bayesian Optimization," Renewable Energy, Elsevier, vol. 127(C), pages 1052-1063.
    7. Marvin Severitt & Paul Manns, 2023. "Efficient Solution of Discrete Subproblems Arising in Integer Optimal Control with Total Variation Regularization," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 869-885, July.
    8. Nash, S. & Phoenix, A., 2017. "A review of the current understanding of the hydro-environmental impacts of energy removal by tidal turbines," Renewable and Sustainable Energy Reviews, Elsevier, vol. 80(C), pages 648-662.
    9. Luciana Casacio & Aurelio R. L. Oliveira & Christiano Lyra, 2018. "Using groups in the splitting preconditioner computation for interior point methods," 4OR, Springer, vol. 16(4), pages 401-410, December.
    10. Stefano Cipolla & Jacek Gondzio, 2023. "Proximal Stabilized Interior Point Methods and Low-Frequency-Update Preconditioning Techniques," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1061-1103, June.
    11. Bittencourt, Tiberio & Ferreira, Orizon Pereira, 2015. "Local convergence analysis of Inexact Newton method with relative residual error tolerance under majorant condition in Riemannian manifolds," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 28-38.
    12. Fatemeh Marzbani & Akmal Abdelfatah, 2024. "Economic Dispatch Optimization Strategies and Problem Formulation: A Comprehensive Review," Energies, MDPI, vol. 17(3), pages 1-31, January.
    13. Martin-Short, R. & Hill, J. & Kramer, S.C. & Avdis, A. & Allison, P.A. & Piggott, M.D., 2015. "Tidal resource extraction in the Pentland Firth, UK: Potential impacts on flow regime and sediment transport in the Inner Sound of Stroma," Renewable Energy, Elsevier, vol. 76(C), pages 596-607.
    14. Fairley, I. & Masters, I. & Karunarathna, H., 2015. "The cumulative impact of tidal stream turbine arrays on sediment transport in the Pentland Firth," Renewable Energy, Elsevier, vol. 80(C), pages 755-769.
    15. Benedetta Morini & Valeria Simoncini & Mattia Tani, 2017. "A comparison of reduced and unreduced KKT systems arising from interior point methods," Computational Optimization and Applications, Springer, vol. 68(1), pages 1-27, September.
    16. Filippo Fabiani & Barbara Franci, 2023. "On Distributionally Robust Generalized Nash Games Defined over the Wasserstein Ball," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 298-309, October.
    17. Yu, Jianxi & Liu, Pei & Li, Zheng, 2021. "Data reconciliation of the thermal system of a double reheat power plant for thermal calculation," Renewable and Sustainable Energy Reviews, Elsevier, vol. 148(C).
    18. Stansby, Peter & Stallard, Tim, 2016. "Fast optimisation of tidal stream turbine positions for power generation in small arrays with low blockage based on superposition of self-similar far-wake velocity deficit profiles," Renewable Energy, Elsevier, vol. 92(C), pages 366-375.
    19. de Groot, Oliver & Mazelis, Falk & Motto, Roberto & Ristiniemi, Annukka, 2021. "A toolkit for computing Constrained Optimal Policy Projections (COPPs)," Working Paper Series 2555, European Central Bank.
    20. David Ek & Anders Forsgren, 2023. "A structured modified Newton approach for solving systems of nonlinear equations arising in interior-point methods for quadratic programming," Computational Optimization and Applications, Springer, vol. 86(1), pages 1-48, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:84:y:2023:i:1:d:10.1007_s10589-022-00386-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.