Seminar 2024-1
Organized by ORIZON PEREIRA FERREIRA
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The seminars in this semester will be held in the Geraldo Ávila Room of IME/UFG, unless otherwise stated. All interested are very welcome to attend.
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Date: April 11
Speaker: Prof. Maurício Silva Louzeiro - IME/UFG
Title: An Adaptive Cubic Regularization quasi-Newton Method on Riemannian Manifolds
Abstract: A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a gradient smaller than $\epsilon_g$ for given $\epsilon_g$, and at most $\mathcal O(\max\{ \epsilon_g^{-\frac{3}{2}}, \epsilon_H^{-3} \})$ iterations to reach a second-order stationary point respectively. Notably, the proposed algorithm remains applicable even in cases of the gradient and Hessian of the objective function unknown. Numerical experiments are performed with gradient and Hessian being approximated by forward finite-differences to illustrate the theoretical results and numerical comparison.
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Date: April 18
Speaker: Prof. Leandro Fonseca Prudente - IME/UFG
Title: Convergência global de um algoritmo BFGS para problemas de otimização multiobjetivo não convexos
Abstract: Propomos um algoritmo BFGS modificado para problemas de otimização multiobjetivo com convergência global, mesmo na ausência de hipóteses de convexidade nas funções objetivo. Além disso, estabelecemos taxa de convergência superlinear local do método sob condições usuais. Nossa abordagem emprega tamanhos de passo satisfazendo as condições de Wolfe e garante que as aproximações Hessianas sejam atualizadas e corrigidas a cada iteração para abordar a falta de suposição de convexidade.
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Date: April 25
Speaker: Thiago Motta - IME/UFG
Title: The Boosted Difference of Convex Functions Algorithm for Nonsmooth Functions
Abstract: In this presentation, we will analyze the paper of Aragón Artacho and Vuong (SIAM J. Optim. https://doi.org/10.1137/18M123339X, 2020) which trata sobre the Boosted Difference of Convex Functions Algorithm (BDCA). It was designed to accelerate the convergence of the classic Difference of Convex Functions Algorithm (DCA) by incorporating an additional line search step. Firstly, it is proof that this scheme can be generalized and effectively applied to certain types of non-smooth DC functions, specifically those expressible as the difference between a smooth function and a potentially non-smooth function. Secondly, it is showed that there is complete flexibility in choosing the test step size for linear search, which can further enhance its performance. It is proven that any limit point of the BDCA iterative sequence is a critical point of the problem under consideration, with the corresponding objective value being monotonically decreasing and convergent. Global convergence and convergence rate of the iterations are established under the Kurdyka–Lojasiewicz property.
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Date: May 2
Speaker: Thiago Motta - IME/UFG
Title: Convergence Rate of an abstract model for Functions Satisfying the Lojasiewicz Inequality.
Abstract: In this talk, we will present a convergence analysis for an abstract model that satisfies a type of sufficient reduction condition and a relative error condition. The convergence analysis depends on the Kurdyka–Lojasiewicz inequality. Specifically, regarding the convergence rate, we consider the desingularizing function given as follows: $\varphi (t)= Mt^{1-q}$, where $q \in [0,1)$ and $M>0$.
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Date: May 9
Speaker: Paulo César Silva Junior
Title:
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Date: May 16
Speaker: Claudemir Rodrigues Santiago- IME/UFG
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Date: May 23
Speaker: Prof. Glaydston C. Bento- IME/UFG
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Date: June 6
Speaker: Prof. Jefferson G. Melo- IME/UFG
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Date: April 13
Speaker: Prof. Maurício Silva Louzeiro - IME/UFG
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Date: June 20
Speaker: Paulo César Silva Junior
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Date: June 27
Speaker: Kelvin Rodrigues Couto - IME/UFG
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Date: July 4
Speaker: Claudemir Rodrigues Santiago- IME/UFG
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Date: July 11
Speaker: Vilmar Gehlen Filho- IME/UFG
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