Bibliography

This bibliography collects every external source cited across this site’s methodology chapters, plus background references that the methodology rests on without quoting. Chapters cite an entry in short form, author and year, linked to the section below that holds it.

For domain terms, see Glossary.

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 Novomodelo 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 Novomodelo. Background reference for SDDP Algorithm, What Novomodelo 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. Background reference for Cut Management, SDDP Algorithm.
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. Background reference for SDDP Algorithm.
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. Background reference for Cut Management.
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 §10.
Dowson, O. (2020). The policy graph decomposition of multistage stochastic programming problems. Networks, 76(1), 3–23. doi:10.1002/net.21932 Defines the policy graph: nodes with local subproblems and cut pools, linked by probability-weighted arcs. Cited in Policy Graphs §4.

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 §7.1.
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 §7.2, §9.

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. Background reference for Risk Measures.
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 §9, §10, Upper Bound Evaluation (References).

Upper Bound Evaluation

Costa, B.F.P. & Leclère, V. (2023). Duality of upper bounds in stochastic dynamic programming. Optimization Online. Preprint: optimization-online.org/?p=23738 Duality framework for inner-approximation upper bounds. Basis for the SIDP inner-approximation estimator described in Upper Bound Evaluation. Cited in Upper Bound Evaluation (References).

Hydro Production

Diniz, A.L. & Maceira, M.E.P. (2008). A four-dimensional model of hydro generation for the short-term hydrothermal dispatch problem considering head and spillage effects. IEEE Transactions on Power Systems, 23(3), 1298–1308. doi:10.1109/TPWRS.2008.922253 The piecewise-linear hydro production model (FPHA) relating storage/head, turbined flow, and spillage to generation. Origin of the approach fitted in Hydro Production Function Models §2 — Novomodelo fits a reduced storage-and-flow variant at spillage = 0, capturing the spillage effect through a lateral-flow secant rather than an explicit spillage axis. Cited in Hydro Production Function Models §2.

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(p) Inflow Model, Scenario Generation.
Hipel, K.W. & McLeod, A.I. (1994). Time Series Modelling of Water Resources and Environmental Systems. Elsevier, Amsterdam. Chapter 14 is the canonical presentation of periodic models: the PAR model definition, the periodic autocovariance/ACF conventions (the more recent observation names the season), the periodic Yule-Walker equations, the lag-0 variance identity, the periodic PACF with its $\pm 1.96/\sqrt{N_m}$ significance band, and the periodic-stationarity condition. Novomodelo’s fitting procedure is this formulation written in correlation form over the $s_m$ -standardized series. Cited in PAR(p) Inflow Model §3.5.
Maceira, M.E.P. & Damázio, J.M. (2006). Use of the PAR(p) model in the stochastic dual dynamic programming optimization scheme used in the operation planning of the Brazilian hydropower system. Probability in the Engineering and Informational Sciences, 20(1), 143–156. doi:10.1017/S0269964806060098 The periodic autoregressive PAR(p) model as fitted inside SDDP for the Brazilian system. Source of the population-divisor seasonal-statistics convention and the iterative AR-order-reduction procedure that keeps composed lag contributions non-negative. Cited in PAR(p) Inflow Model §3.2, §3.6, §7.6.
Treistman, F., Maceira, M.E.P., Damázio, J.M. & Cruz, C.B. (2020). Periodic time series model with annual component applied to operation planning of hydrothermal systems. In 2020 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS), Liège, Belgium, 1–6. doi:10.1109/PMAPS47429.2020.9183472 The PAR(p)-A model: the periodic autoregressive model augmented with an annual component, a regression term on the rolling annual average (the mean of the twelve previous monthly inflows), which extends the model’s memory to long dry and wet periods. Cited in PAR(p) Inflow Model §7.
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 clamp-plus-slack formulation. Cited in Inflow Non-Negativity Solution Methods §8.
Maceira, M.E.P., Terry, L.A., Costa, F.S., Damázio, J.M. & Melo, A.C.G. (2002). 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), Seville, Spain. The NEWAVE / DECOMP / GEVAZP optimization chain for the Brazilian system. Source of the DECOMP-style scenario tree — a deterministic trunk with branching at the final stage — expressed as a terminal fan of sibling nodes traversed by enumerated selection. Cited in Scenario Generation §6.

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 $\tau(t)$ , the cycle convergence inequality, the season-indexed cut pool with its cut-sharing equation, and the fixed-point Bellman operator of the reserved cyclic design that Horizon Modes describes. Cited in Horizon Modes §6.

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 the sampling-scheme abstractions, the convex-combination risk-measure structure and the notation conventions in Novomodelo. Cited in Notation Conventions, Scenario Generation §3, Risk Measures §3, Policy Graphs §4.
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 Novomodelo’s default LP solver. Background reference for LP Warm-Start.

Numerical Methods

Curtis, A.R. & Reid, J.K. (1972). On the automatic scaling of matrices for Gaussian elimination. IMA Journal of Applied Mathematics, 10(1), 118–124. doi:10.1093/imamat/10.1.118 Iterative least-squares matrix scaling for Gaussian elimination. Novomodelo’s own prescaler is a one-pass geometric-mean row/column equilibration in the same family; the LP backend’s optional solver_scaling profile applies the Curtis–Reid algorithm. Cited in LP Layout and Scaling §2.
Higham, N.J. (2002). Computing the nearest correlation matrix — a problem from finance. IMA Journal of Numerical Analysis, 22(3), 329–343. doi:10.1093/imanum/22.3.329 The nearest positive-semidefinite / correlation-matrix problem underlying the clip-negative-eigenvalues projection used when factorising the spatial correlation matrix. Cited in PAR(p) Inflow Model §6.

Brazilian Power-System Context

CEPEL — Centro de Pesquisas de Energia Elétrica (n.d.). Documentação Técnica dos modelos para Planejamento da Operação do SIN – Ambiente Libs. Online manual: see.cepel.br/manual/libs/latest/ Official documentation of the NEWAVE / DECOMP / DESSEM suite of stochastic-dispatch models operated for the Brazilian system. Cited only for practitioner terms and notation: the equivalent-terms tables of the glossary, the GEVAZP residual distribution (section Distribuição Lognormal 3 parâmetros) and the PAR(p) notation (section Modelo Autorregressivo Periódico - Par(p)). The methods those models implement are credited to their primary articles above: FPHA → Diniz & Maceira (2008); PAR(p) and iterative order reduction → Maceira & Damázio (2006); PAR(p)-A → Treistman et al. (2020); DECOMP-style scenario tree → Maceira et al. (2002). Novomodelo’s dead-volume filling model is its own and is not attributed here. Cited in Glossary — Brazilian Power-System Ecosystem and Glossary — Equivalent terms in other planning tools.