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Dual Dynamic Programing with cut selection: Convergence proof and numerical experiments

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  • Guigues, Vincent

Abstract

We consider convex optimization problems formulated using dynamic programing equations. Such problems can be solved using the Dual Dynamic Programing algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to select the most relevant Benders cuts. We propose a limited memory variant of Level 1 and show the convergence of DDP combined with the Territory algorithm, Level 1 or its variant for nonlinear optimization problems. In the special case of linear programs, we show convergence in a finite number of iterations. Numerical simulations illustrate the interest of our variant and show that it can be much quicker than a simplex algorithm on some large instances of portfolio selection and inventory problems.

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  • Guigues, Vincent, 2017. "Dual Dynamic Programing with cut selection: Convergence proof and numerical experiments," European Journal of Operational Research, Elsevier, vol. 258(1), pages 47-57.
    • Handle: RePEc:eee:ejores:v:258:y:2017:i:1:p:47-57
    DOI: 10.1016/j.ejor.2016.10.047
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    References listed on IDEAS

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    1. Vincent Guigues, 2014. "SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning," Computational Optimization and Applications, Springer, vol. 57(1), pages 167-203, January.
    2. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    3. Alexander Shapiro & Wajdi Tekaya & Murilo Pereira Soares & Joari Paulo da Costa, 2013. "Worst-Case-Expectation Approach to Optimization Under Uncertainty," Operations Research, INFORMS, vol. 61(6), pages 1435-1449, December.
    4. Philpott, A.B. & de Matos, V.L., 2012. "Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion," European Journal of Operational Research, Elsevier, vol. 218(2), pages 470-483.
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    Cited by:

    1. Michelle Bandarra & Vincent Guigues, 2021. "Single cut and multicut stochastic dual dynamic programming with cut selection for multistage stochastic linear programs: convergence proof and numerical experiments," Computational Management Science, Springer, vol. 18(2), pages 125-148, June.
    2. Guigues, Vincent & Shapiro, Alexander & Cheng, Yi, 2023. "Duality and sensitivity analysis of multistage linear stochastic programs," European Journal of Operational Research, Elsevier, vol. 308(2), pages 752-767.
    3. Lorenzo Reus & Guillermo Alexander Sepúlveda-Hurtado, 2023. "Foreign exchange trading and management with the stochastic dual dynamic programming method," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-38, December.
    4. Haodong Yu & Jie Sun & Yanjun Wang, 2021. "A time-consistent Benders decomposition method for multistage distributionally robust stochastic optimization with a scenario tree structure," Computational Optimization and Applications, Springer, vol. 79(1), pages 67-99, May.
    5. D. Ávila & A. Papavasiliou & N. Löhndorf, 2022. "Parallel and distributed computing for stochastic dual dynamic programming," Computational Management Science, Springer, vol. 19(2), pages 199-226, June.
    6. Vincent Guigues & Renato D. C. Monteiro, 2021. "Stochastic Dynamic Cutting Plane for Multistage Stochastic Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 513-559, May.
    7. Liu, Rui Peng & Shapiro, Alexander, 2020. "Risk neutral reformulation approach to risk averse stochastic programming," European Journal of Operational Research, Elsevier, vol. 286(1), pages 21-31.

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