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As a follow-up of the industrial problems dealt with in 2018, 2019, 2021 and 2022, in partnership with CCEE and CEPEL, in 2023 the study group Energy planning and environmental constraints focused on the impact that prioritizing multiple uses of water has on the electric energy production systems, specially in predominantly hydro systems, which is the case of Brazil. In order to model environmental constraints in the long-term hydrothermal generation planning problem, the resulting large-scale multi-stage linear programming problem was modelled in JuMP and solved by stochastic dual dynamic programming. To assess if the development represented well the behavior of the Brazilian power system, the Julia formulation first was benchmarked with Brazil s official model, Newave. Environmental constraints were introduced in this problem by two different approaches, one that represents the multiple uses of water by means of 0-1 variables, and another one that makes piecewise linear approximations of the relevant constraints. Numerical results show that penalties of slack variables strongly affect the obtained water values., Comment: 39 pages, 22 figures

During the early months of the current COVID-19 pandemic, social-distancing measures effectively slowed disease transmission in many countries in Europe and Asia, but the same benefits have not been observed in some developing countries such as Brazil. In part, this is due to a failure to organise systematic testing campaigns at nationwide or even regional levels. To gain effective control of the pandemic, decision-makers in developing countries, particularly those with large populations, must overcome difficulties posed by an unequal distribution of wealth combined with low daily testing capacities. The economic infrastructure of the country, often concentrated in a few cities, forces workers to travel from commuter cities and rural areas, which induces strong nonlinear effects on disease transmission. In the present study, we develop a smart testing strategy to identify geographic regions where COVID-19 testing could most effectively be deployed to limit further disease transmission. The strategy uses readily available anonymised mobility and demographic data integrated with intensive care unit (ICU) occupancy data and city-specific social-distancing measures. Taking into account the heterogeneity of ICU bed occupancy in differing regions and the stages of disease evolution, we use a data-driven study of the Brazilian state of Sao Paulo as an example to show that smart testing strategies can rapidly limit transmission while reducing the need for social-distancing measures, thus returning life to a so-called new normal, even when testing capacity is limited.

In Variational Analysis, VU-theory provides a set of tools that is helpful for understanding and exploiting the structure of nonsmooth functions. The theory takes advantage of the fact that at any point, the space can be separated into two orthogonal subspaces: one that describes the direction of nonsmoothness of the function, and the other on which the function behaves smoothly and has a gradient. For a composite function, this work establishes a chain rule that facilitates the computation of such gradients and characterizes the smooth subspace under reasonable conditions. From the chain rule presented, formulas for the separation, smooth perturbation and sum of functions are provided. Several nonsmooth examples are explored, including norm functions, max-of-quadratic functions and LASSO-type regularizations., Comment: 28 pages including references

The $\mathcal{VU}$-algorithm is a superlinearly convergent method for minimizing nonsmooth, convex functions. At each iteration, the algorithm works with a certain $\mathcal{V}$-space and its orthogonal $\U$-space, such that the nonsmoothness of the objective function is concentrated on its projection onto the $\mathcal{V}$-space, and on the $\mathcal{U}$-space the projection is smooth. This structure allows for an alternation between a Newton-like step where the function is smooth, and a proximal-point step that is used to find iterates with promising $\mathcal{VU}$-decompositions. We establish a derivative-free variant of the $\mathcal{VU}$-algorithm for convex finite-max objective functions. We show global convergence and provide numerical results from a proof-of-concept implementation, which demonstrates the feasibility and practical value of the approach. We also carry out some tests using nonconvex functions and discuss the results.