On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems
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We consider well-known decomposition techniques for multistage stochastic programming and a new scheme based on normal solutions for stabilizing iterates during the solution process. The given algorithms combine ideas from finite perturbation of convex programs and level bundle methods to regularize the so-called forward step of these decomposition methods. Numerical experiments on a hydrothermal scheduling problem indicate that our algorithms are competitive with the state-of-the-art approaches such as multistage regularized decomposition, nested decomposition and stochastic dual dynamic programming.
KeywordsNormal solution SDDP algorithm Stochastic optimization Nonsmooth optimization
We would like to acknowledge the coordinating editor and two anonymous referees for their constructive suggestions that considerably improved the original version of this article. We also thank C. Wolf and A. Koberstein for providing us with some test problems and E. Finardi and F. Beltrán for the instances of the multistage hydro-thermal power generation planning problem. Finally, the first and the second authors would like to acknowledge the partial financial support of PGMO (Gaspard Monge Program for Optimization and operations research) of the Hadamard Mathematics Foundation, through the project “Models for planning energy investment under uncertainty”. The third author acknowledges partial support by the National Science Foundation (NSF) under grant CMMI 1854960. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.
- 17.Dupačová, J.: Portfolio Optimization and Risk Management via Stochastic Programming. Osaka University Press, Osaka (2009)Google Scholar
- 18.Fábián, C.I.: Bundle-type methods for inexact data. In: Proceedings of the XXIV Hungarian Operations Researc Conference (Veszprém, 1999). Special issue, T. Csendes and T. Rapcsák (eds.), vol. 8, pp. 35–55, (2000)Google Scholar
- 20.Fhoula, B., Hajji, A., Rekik, M.: Stochastic dual dynamic programming for transportation planning under demand uncertainty. In: 2013 International Conference on Advanced Logistics and Transport, pp. 550–555, May (2013)Google Scholar
- 25.Hindsberger, M., Philpott, A.B.: Resa: A method for solving multi-stage stochastic linear programs. In: SPIX Stochastic Programming Symposium, Berlin (2001)Google Scholar
- 26.Holmes, D.: A (po)rtable (s)tochastic programming (t)est (s)et (posts). http://users.iems.northwestern.edu/~jrbirge/html/dholmes/post.html (1995)
- 33.Lemaréchal, C.: Constructing bundle methods for convex optimization. In: Hiriart-Urruty, J. B. (ed.) Fermat Days 85: Mathematics for Optimization. North-Holland Mathematics Studies, vol. 129, pp. 201–240. North-Holland (1986)Google Scholar
- 36.Maceira, M.E.P., Terry, L.A., Costa, F.S., Damázio, J.M., Melo, A.C.G.: Chain of optimization models for setting the energy dispatch and spot price in the Brazilian system. In: Proceedings of the 14th Power Systems Computation Conference—PSCC, pp. 1–7. Servilla, Spain (2002)Google Scholar
- 41.Ch Pflug, G., Römisch, W.: Modeling. Measuring and Managing Risk. World Scientific, Singapore (2007). https://www.worldscientific.com/worldscibooks/10.1142/6478
- 48.Shapiro, A., Dentcheva, D., Ruszczyński, A.: Lectures on stochastic programming. Modeling and Theory. MPS-SIAM Series on Optimization. SIAM and MPS, vol. 9. Philadelphia, (2009)Google Scholar