Bernardo Costa

Bernardo Costa

Professor at FGV EMAp, Optimization

Publications

You can also find my articles on my Google Scholar profile.

Journal Articles

Stochastic optimal control with control-dependent diffusion and state constraints: A degenerate elliptic approach

Published in , 2026

We combine the analysis of degenerate elliptic Hamilton–Jacobi–Bellman equations with control-dependent diffusion and state constraints to provide a unified framework for stochastic optimal control problems. We prove that the associated optimal value function is the unique viscosity solution of the HJB equation with a nontrivial Neumann boundary condition.

Recommended citation: Anderson O. Calixto, Bernardo Freitas Paulo da Costa, Glauco Valle. Stochastic optimal control with control-dependent diffusion and state constraints: A degenerate elliptic approach. Mathematical Control and Related Fields. https://doi.org/10.3934/mcrf.2026027
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Multiscale Stochastic Control With Domain Restriction in the Slow Variable

Published in Journal of Optimization Theory and Applications, 2026

We combine singular perturbation theory and viscosity solutions to provide an effective HJB equation for slow variables subject to state constraints and boundary reflection with penalization. In special cases, we also show how to reconstruct an effective optimal control problem on the slow variables.

Recommended citation: Anderson de Oliveira Calixto, Bernardo Freitas Paulo da Costa & Glauco Valle. Multiscale Stochastic Control With Domain Restriction in the Slow Variable. Journal of Optimization Theory and Applications 209, 54 (2026). https://doi.org/10.1007/s10957-026-03001-6
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Risk budgeting portfolios from simulations

Published in European Journal of Operational Research, 2023

Algorithms for building risk budgeting portfolios from simulations of returns with coherent risk measures, such as Expected Shortfall.

Recommended citation: B. Freitas Paulo da Costa, Silvana M. Pesenti, Rodrigo S. Targino. "Risk budgeting portfolios from simulations". European Journal of Operational Research, 311(3), 2023, 1040-1056.
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Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations

Published in Journal of Theoretical Probability, 2023

We extend the construction of reaction–diffusion models to provide scaling limits as SDEs in infinite graphs.

Recommended citation: C. da Costa, B. Freitas Paulo da Costa, D. Valesin. "Reaction–Diffusion Models for a Class of Infinite-Dimensional Nonlinear Stochastic Differential Equations". Journal of Theoretical Probability, 36(2), 2023, 1059-1087.
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Dual SDDP for risk-averse multistage stochastic programs

Published in Operations Research Letters, 2023

Dual SDDP and deterministic upper bounds for risk-averse multistage stochastic programs.

Recommended citation: B. F. P. da Costa, V. Leclere. "Dual SDDP for risk-averse multistage stochastic programs". Operations Research Letters, 51(3), 2023, 332-337.
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Stochastic Lipschitz dynamic programming

Published in Mathematical Programming, 2020

Non-convex approximation of the cost-to-go functions in multistage stochastic mixed integer linear programming.

Recommended citation: S. Ahmed, F. G. Cabral, B. F. P. da Costa. "Stochastic Lipschitz dynamic programming". Mathematical Programming, 191, 2022, 755-793.
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Reaction–Diffusion models: From particle systems to SDE’s

Published in Stochastic Processes and their Applications, 2019

A construction of a family of Reaction–Diffusion models that converge after scaling to the solution to a non-linear V-dimensional SDE.

Recommended citation: C. da Costa, B. F. P. da Costa, M. Jara. "Reaction–Diffusion models: From particle systems to SDE's". Stochastic Processes and their Applications 129 (2019), no. 11, p. 4411-4430.
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Sur les courbes de Brody dans P^n(C)

Published in Mathematische Annalen, 2012

Nevanlinna theory and defect relations for Brody curves in projective spaces.

Recommended citation: B. F. P. Da Costa, J. Duval. "Sur les courbes de Brody dans $P^n(\mathbf C)$". Mathematische Annalen 355 (2013), no. 4, p. 1593-1600.
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Conference Papers

Get rid of your constraints and reparametrize: A study in NNLS and implicit bias

Published in The 28th International Conference on Artificial Intelligence and Statistics, 2025

We link overparametrized gradient descent to a Riemannian optimization problem, and prove global convergence to NNLS solutions. We moreover show this reparametrization favors sparse solutions, and study acceleration mechanisms.

Recommended citation: Hung-Hsu Chou, Johannes Maly, Claudio Mayrink Verdun, Bernardo Freitas Paulo da Costa, Heudson Mirandola. "Get rid of your constraints and reparametrize: A study in NNLS and implicit bias". In: Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025.
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O Dilema na Alocação de Energia Firme: Vazões Totais contra Incrementais em Cascatas Hidrelétricas

Published in LVI Simpósio Brasileiro de Pesquisa Operacional, 2024

Uma discussão sobre a definição de Energia Firme de usinas hidrelétricas em cascata, do ponto de vista da teoria dos jogos.

Recommended citation: Rafael Benchimol Klausner, Joaquim Dias Garcia, Bernardo Freitas Paulo da Costa, Alexandre Street, Sérgio Granville. "O Dilema na Alocação de Energia Firme: Vazões Totais contra Incrementais em Cascatas Hidrelétricas". In: Anais do LVI Simpósio Brasileiro de Pesquisa Operacional, 2024, Fortaleza.
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Boundary Conditions for Hydrothermal Operation Planning Problems: The Infinite Horizon Approach

Published in XLIII Congresso Nacional de Matemática Aplicada e Computacional, 2024

Using periodic models to improve the long-term planning of hydrothermal operation and inform expansion planning.

Recommended citation: BFP da Costa et al. "Boundary Conditions for Hydrothermal Operation Planning Problems: The Infinite Horizon Approach". XLIII Congresso Nacional de Matemática Aplicada e Computacional, Porto de Galinhas, PE, 16–20 Setembro 2024.
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