arXiv subjects

Luís Felipe Bueno

Publications and source records attributed to Luís Felipe Bueno.

4 recordsLinked to original sources

arXiv2026

Inexact Adjoint Gradients and Directional Tolerances for Full-Potential Airfoil Optimization

This paper develops a framework connecting discrete adjoint gradient-error analysis with an optimization method that uses directional error tolerances, and applies it to airfoil shape optimization governed by a conservative full-potential flow solver on body-fitted structured meshes. The theoretical part derives the reduced discrete adjoint formula for scalar objectives constrained by a state equation and analyzes how inexact state and adjoint residuals propagate into the reduced gradient. For residuals that are affine in the state variable, the gradient error is bounded by a linear combination of the state and adjoint residual tolerances. On compact sets of decision variables, a uniform version of this bound is obtained, leading to a directional tolerance condition under which the inexact gradient satisfies an exact descent inequality. The resulting inexact general directions method inherits convergence properties under uniformly bounded, diminishing, and Armijo-type step-size rules. The computational part combines a parabolic initial grid generator, an elliptic mesh smoother, and a full-potential discretization with artificial-density stabilization and approximate-factorization iteration. The optimization problem is formulated as a pressure-matching problem in which a class-shape-transformation airfoil parametrization is adjusted so that the computed surface pressure coefficient approaches prescribed reference data, subject to mesh-generation and full-potential residual constraints.

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arXiv2025

An Inexact General Descent Method with Applications in Differential Equation-Constrained Optimization

In many applications, gradient evaluations are inherently approximate, motivating the development of optimization methods that remain reliable under inexact first-order information. A common strategy in this context is adaptive evaluation, whereby coarse gradients are used in early iterations and refined near a minimizer. This is particularly relevant in differential equation-constrained optimization (DECO), where discrete adjoint gradients depend on iterative solvers. Motivated by DECO applications, we propose an inexact general descent framework and establish its global convergence theory under two step-size regimes. For bounded step sizes, the analysis assumes that the error tolerance in the computed gradient is proportional to its norm, whereas for diminishing step sizes, the tolerance sequence is required to be summable. The framework is implemented through inexact gradient descent and an inexact BFGS-like method, whose performance is demonstrated on a second-order ODE inverse problem and a two-dimensional Laplace inverse problem using discrete adjoint gradients with adaptive accuracy. Across these examples, adaptive inexact gradients consistently reduced optimization time relative to fixed tight tolerances, while incorporating curvature information further improved overall efficiency.

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arXiv2025

A Jacobi-type Newton method for Nash equilibrium problems with descent guarantees

A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton's method to the system of nonlinear equations obtained by the corresponding first-order necessary optimality conditions. However, when taking into account the game dynamics, it is not clear what is the goal of each player when considering that they are taking their current decision following Newton's iterates. In this paper we provide an interpretation for Newton's iterate in view of the game dynamics as follows: instead of minimizing the quadratic approximation of their objective function parameterized by the other player current decision (as a typical Jacobi-type strategy), we show that the Newton iterate follows this approach but with the objective function parameterized by a prediction of the other player action, considering that they are following the same Newtonian strategy. This interpretation allows us to present a new Newtonian algorithm where a backtracking procedure is introduced in order to guarantee that the computed Newtonian directions, for each player, are descent directions for their corresponding parameterized functions. Thus, besides favoring global convergence, our algorithm also favors true minimizers instead of maximizers or saddle points, differently from the standard Newton method, which does not consider the minimization structure of the problem in the non-convex case. Thus, our method is more robust in comparison with other Jacobi-type strategies or the pure Newtonian approach, which is corroborated by our illustrative numerical experiments. We also present a proof of the well-definiteness of the algorithm under some standard assumptions, together with a thorough analysis of its convergence properties taking into account the game dynamics.

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arXiv2023

Impact of environmental constraints in hydrothermal energy planning

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.

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