Recent Advances on Derivative-Free Optimization - Prof. Geovani Grapiglia

O seminário será em portugues.
Abstract:
Optimization problems are ubiquitous in Applied Mathematics. They appear in decision-making problems, in
the design of efficient devices and also in the calibration of mathematical models. Iterative methods for nonlinear optimization generate sequences of approximations obtained by the minimization of simpler local models. In standard optimization methods, local models are built using derivatives of the functions that define the problem. However, in many practical situations, these derivatives are not readily available. This happens, for example, when the function values are obtained as the result of some black box computer simulation. These problems can be addressed using Derivative-Free Optimization methods, which are methods that rely only on function evaluations. In this talk I will present some recent results about the worst-case complexity of derivative-free methods.

Short Bio:
Prof. Geovani Nunes Grapiglia se doutorou em Matemática em 2014 pela Universidade Federal do Paraná, onde foi professor de 2015 a 2021. Desde 2022 ocupa a cátedra que foi do Prof. Yurii Nesterov na Université Catholique de Louvain (Louvain-la-Neuve), Bélgica.
Sua pesquisa cobre o desenvolvimento, a análise e a aplicação de métodos de otimização.
Seus trabalhos recentes estão associados com os métodos sem-derivada para otimização, visando à aceleração dos métodos de grande porte para a otimização convexa.
Alguns dos seus últimos trabalhos:
1-GRAPIGLIA, G, N.; Quadratic regularization methods with finite-difference gradients. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 85, p. 683-703, 2023.
2-FERREIRA, O. P.; GRAPIGLIA, G. N.; SANTOS, E. M. ; SOUZA, J. C. O. . A subgradient method with non-monotone line search. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 84, p. 397-420, 2023.
3-GRAPIGLIA, G. N.. Worst-Case Evaluation Complexity of a Quadratic Penalty Method for Nonconvex Optimization. OPTIMIZATION METHODS & SOFTWARE, v. 38, p. 781-803, 2023.
4-GRAPIGLIA, G. N.; STELLA, G. F. D.. An Adaptive Riemannian Gradient Method Without Function Evaluations. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 197, p. 1140-1160, 2023.
5-GRAPIGLIA, G. N.; NESTEROV, YURII. Adaptive Third-Order Methods for Composite Convex Optimization. SIAM JOURNAL ON OPTIMIZATION, v. 33, p. 1855-1883, 2023.
6-GRAPIGLIA, G.N.; NESTEROV, YURII. Tensor methods for finding approximate stationary points of convex functions. OPTIMIZATION METHODS & SOFTWARE, v. 37, p. 605-638, 2022.