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Bibliography

Core references for the algorithms and methods implemented in Cobre.

SDDP Foundations

  • Benders, J.F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238–252. — The original Benders decomposition paper. Foundation for the L-shaped method and SDDP.

  • Birge, J.R. (1985). Decomposition and partitioning methods for multistage stochastic linear programs. Operations Research, 33(5), 989–1007. — Multi-cut formulation for stochastic programs. Origin of the multi-cut L-shaped method.

  • Birge, J.R. & Louveaux, F.V. (2011). Introduction to Stochastic Programming. Springer, 2nd edition. — Standard textbook reference for stochastic programming theory and decomposition methods.

  • Pereira, M.V.F. & Pinto, L.M.V.G. (1991). Multi-stage stochastic optimization applied to energy planning. Mathematical Programming, 52(1–3), 359–375. — The original SDDP paper. Foundational for everything in cobre-sddp.

  • Philpott, A.B. & Guan, Z. (2008). On the convergence of stochastic dual dynamic programming and related methods. Operations Research Letters, 36(4), 450–455. — Convergence theory for SDDP.

  • Costa, B.F.P., Calixto, A.O., Sousa, R.F.S., Figueiredo, R.T., Penna, D.D.J., Khenayfis, L.S. & Oliveira, A.M.R. (2025). Boundary conditions for hydrothermal operation planning problems: the infinite horizon approach. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 11(1), 1–7. doi:10.5540/03.2025.011.01.0355 — Infinite horizon boundary conditions for hydrothermal planning. Related to the infinite horizon extension in cobre-sddp.

Cut Management and Performance

  • de Matos, V.L., Philpott, A.B. & Finardi, E.C. (2015). Improving the performance of Stochastic Dual Dynamic Programming. Journal of Computational and Applied Mathematics, 290, 196–208. — Cut selection strategies. Basis for the cut selection in cobre-sddp.

  • Bandarra, M. & Guigues, V. (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, 18(2), 125–148. doi:10.1007/s10287-021-00387-8. Preprint: arXiv:1902.06757 — Convergence proof for Level-1 and LML1 cut selection strategies. Guarantees finite convergence with probability 1.

Risk Measures

  • Shapiro, A. (2011). Analysis of stochastic dual dynamic programming method. European Journal of Operational Research, 209(1), 63–72. — Convergence analysis, complexity bounds, and risk-averse extensions (including CVaR) for SDDP.

  • Philpott, A.B. & de Matos, V.L. (2012). Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion. European Journal of Operational Research, 218(2), 470–483. — Dynamic sampling with risk aversion and Markovian scenario transitions.

  • Philpott, A.B., de Matos, V.L. & Finardi, E.C. (2013). On solving multistage stochastic programs with coherent risk measures. Operations Research, 61(4), 957–970. doi:10.1287/opre.2013.1175 — Time-consistent risk-averse SDDP with CVaR. Dual representation for risk-averse cut generation and nested risk measures.

Upper Bound and Inner Approximation

  • Costa, B.F.P. & Leclere, V. (2023). Duality of upper bounds in stochastic dynamic programming. Optimization Online. optimization-online.org/?p=23738 — Duality framework for upper bounds in stochastic dynamic programming. Basis for the upper bound evaluation in cobre-sddp.

Inflow Modeling

  • Larroyd, P.V., Pedrini, R., Beltran, F., Teixeira, G., Finardi, E.C. & Picarelli, L.B. (2022). Dealing with Negative Inflows in the Long-Term Hydrothermal Scheduling Problem. Energies, 15(3), 1115. doi:10.3390/en15031115 — Inflow non-negativity treatment for PAR(p) models in hydrothermal dispatch.

Software References

  • Dowson, O. & Kapelevich, L. (2021). SDDP.jl: A Julia Package for Stochastic Dual Dynamic Programming. INFORMS Journal on Computing, 33(1), 27–33. — Algorithmic reference for SDDP.jl. Influenced cut management and risk measure implementation in Cobre.

Brazilian Power System

Solver

  • Huangfu, Q. & Hall, J.A.J. (2018). Parallelizing the dual revised simplex method. Mathematical Programming Computation, 10, 119–142. — HiGHS simplex implementation. Cobre uses HiGHS as its default LP solver.