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Cobre Cobre Cobre Methodology Reference

Bibliography

This bibliography collects every external source — papers, books, preprints, and software references — cited in the methodology chapters of this book. Each entry lists the chapters that depend on it; foundational works that underlie the methodology without being directly quoted are included as background references.

For a glossary of domain terms used throughout the book, see Glossary.

SDDP Foundations

Section titled “SDDP Foundations”

  • Benders, J.F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238–252. doi:10.1007/BF01386316 The original Benders decomposition paper. Foundation for the L-shaped method and SDDP. Background reference for SDDP Algorithm, Cut Management, What Cobre Solves.

  • 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. doi:10.1007/BF01582895 The original SDDP paper. Foundational for the entire algorithm and for the hydrothermal-dispatch application that motivates Cobre. Background reference for SDDP Algorithm, What Cobre Solves.

  • Birge, J.R. (1985). Decomposition and partitioning methods for multistage stochastic linear programs. Operations Research, 33(5), 989–1007. doi:10.1287/opre.33.5.989 Multi-cut formulation for stochastic programs. Origin of the multi-cut L-shaped method that the single-cut formulation in Cut Management is contrasted with.

  • Birge, J.R. & Louveaux, F.V. (2011). Introduction to Stochastic Programming, 2nd edition. Springer. doi:10.1007/978-1-4614-0237-4 Standard textbook reference for stochastic programming theory and decomposition methods.

  • Philpott, A.B. & Guan, Z. (2008). On the convergence of stochastic dual dynamic programming and related methods. Operations Research Letters, 36(4), 450–455. doi:10.1016/j.orl.2008.01.013 Convergence theory for SDDP under finitely many scenarios.

  • Shapiro, A. (2011). Analysis of stochastic dual dynamic programming method. European Journal of Operational Research, 209(1), 63–72. doi:10.1016/j.ejor.2010.08.007 Convergence analysis, complexity bounds, and risk-averse extensions for SDDP. Cited in Risk Measures §11.

Cut Management and Convergence

Section titled “Cut Management and Convergence”

  • 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. doi:10.1016/j.cam.2015.04.048 Cut selection strategies for SDDP, including the Level-1 active-cut criterion. Cited in Cut Management §6.

  • 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. Cited in Cut Management §6.

Risk Measures

Section titled “Risk Measures”

  • Rockafellar, R.T. & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2(3), 21–41. doi:10.21314/JOR.2000.038 Definition of CVaR and the linearisation that allows it to be embedded in linear programmes — the basis for risk-averse cut aggregation in SDDP. Background reference for Risk Measures.

  • 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. doi:10.1016/j.ejor.2011.10.056 Dynamic sampling under risk aversion with 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 and aggregation weights for risk-averse cut generation. Cited in Risk Measures §11 and Upper Bound Evaluation §12.

Upper Bound Evaluation

Section titled “Upper Bound Evaluation”

Inflow Modelling

Section titled “Inflow Modelling”

  • Box, G.E.P. & Jenkins, G.M. (1976). Time Series Analysis: Forecasting and Control, revised edition. Holden-Day, San Francisco. Foundational textbook for ARMA / autoregressive time-series modelling and the Yule-Walker estimation method that underlies the PAR(p) fitting procedure. Background reference for PAR Inflow Model, Scenario Generation.

  • Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. doi:10.1109/TAC.1974.1100705 Akaike Information Criterion (AIC) used for AR-order selection in the PAR(p) model. Cited in PAR Inflow Model §4.2.

  • Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. doi:10.1214/aos/1176344136 Bayesian Information Criterion (BIC) used as an alternative AR-order selection criterion. Cited in PAR Inflow Model §4.3.

  • 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 — the reference design that motivates the production clamp-plus-slack formulation. Cited in Inflow Non-Negativity §8.

Boundary Conditions and Horizon Modes

Section titled “Boundary Conditions and Horizon Modes”
  • 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 Periodic policy graph and infinite-horizon SDDP formulation. Source of the season function τ(t)\tau(t), the cycle convergence inequality, the season-indexed cut pool with its cut-sharing equation, and the fixed-point Bellman operator used in the cyclic-mode treatment. Cited in Horizon Modes §6.

Software References

Section titled “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. doi:10.1287/ijoc.2020.0987. Documentation: sddp.dev. Reference SDDP implementation in Julia. Influenced cut-management patterns, sampling-scheme abstractions, the state-pinning cut-extraction technique (realised in Cobre via column bounds and reduced costs), and notation conventions in Cobre. Cited in Notation Conventions, LP Formulation §11, Cut Management §2, Scenario Generation §10, Risk Measures §3.

  • Huangfu, Q. & Hall, J.A.J. (2018). Parallelizing the dual revised simplex method. Mathematical Programming Computation, 10(1), 119–142. doi:10.1007/s12532-017-0130-5 HiGHS dual simplex implementation. HiGHS is Cobre’s default LP solver.

Brazilian Power-System Context

Section titled “Brazilian Power-System Context”
  • CEPEL Technical Documentation. Centro de Pesquisas de Energia Elétrica. Online manual: see.cepel.br/manual/libs/latest/. Official documentation for the NEWAVE / DECOMP / DESSEM suite of stochastic-dispatch models used by the Brazilian system operator. Source of the FPHA terminology (q_lat, q_out, enchimento de volume morto), the reducao_ordem algorithm for PAR-order reduction, and the DECOMP-style scenario tree. Cited in Hydro Production Models §1, Penalty System §6, PAR Inflow Model §4.1, Scenario Generation §6.2.

Third-party notices

© 2026 Cobre Contributors — text & figures CC-BY-4.0, code Apache-2.0