Seminar 2024-2
Organized by MAURICIO SILVA LOUZEIRO
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All interested are very welcome.
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Date: September 5
Local: Classroom at IME-UFG
Time: 8:30 am to 9:50 am
Speaker: Prof. Max Leandro Nobre Gonçalves (Professor at IME-UFG)
Title: An away-step Frank-Wolfe algorithm for constrained multiobjective optimization
Abstract: In this talk, we propose and analyze an away-step Frank–Wolfe algorithm designed for solving multiobjective optimization problems over polytopes. We prove that each limit point of the sequence generated by the algorithm is a weak Pareto optimal solution. Furthermore, under additional conditions, we show linear convergence of the whole sequence to a Pareto optimal solution. Numerical examples illustrate a promising performance of the proposed algorithm in problems where the multiobjective Frank–Wolfe convergence rate is only sublinear.
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Date: September 12
Local: Auditorium at IME-UFG
Time: 4:10 pm to 5:30 pm
Speaker: Prof. Alexandru Kristály (Professor at Babeş-Bolyai University, Romenia)
Title: From Optimal Transportation to Sharp Geometric Inequalities: Euclidean vs. non-Euclidean
Abstract: We are going to apply Optimal Transportation theory to provide sharp geometric inequalities on Euclidean and non-Euclidean spaces, including Riemannian and Finsler manifolds or even not necessarily smooth metric measure spaces satisfying certain curvature-dimension conditions in the sense of Lott-Sturm-Villani. As applications, we prove sharp Sobolev and Faber-Krahn inequalities on such structures.
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Date: September 19
Local: Classroom at IME-UFG
Time: 8:30 am to 9:50 am
Speaker: Claudemir Rodrigues Santiago (PHD student at UFG)
Title: Propriedades de Convergência de um Método Proximal Gradiente não Monótono
Abstract: Nesta palestra, serão apresentados resultados do paper Kanzow, C. and Mehlitz, P.: Convergence Properties of Monotone and Nonmonotone
Proximal Gradient Methods Revisited; JOTA, no. 195: 624–646, (2022). Especificamente, discutiremos a convergência do algoritmo de gradiente
proximal não monótono aplicado à minimização de uma função f continuamente diferenciável somada a uma função não-suave g, o que corresponde a
minimização "composite" não convexa.
Proximal Gradient Methods Revisited; JOTA, no. 195: 624–646, (2022). Especificamente, discutiremos a convergência do algoritmo de gradiente
proximal não monótono aplicado à minimização de uma função f continuamente diferenciável somada a uma função não-suave g, o que corresponde a
minimização "composite" não convexa.
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Date: October 3
Local: Classroom at IME-UFG
Time: 8:30 am to 9:50 am
Speaker: Prof. Maurício Silva Louzeiro (Professor at IME-UFG)
Title: Inexact Newton Methods for Solving Generalized Equations on Riemannian Manifolds
Abstract: The convergence of inexact Newton methods is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property, which is also explored. Under appropriate conditions and without any additional geometric assumptions, local convergence results with linear and quadratic rates, as well as a semi-local convergence result, are obtained for the proposed method. Finally, the theory is applied to the problem of finding a singularity for the sum of two vector fields. In particular, the KKT system for the constrained Riemannian center of mass on the sphere is explored numerically.
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Date: October 10
Local: Classroom at IME-UFG
Time: 8:30 am to 9:50 am
Speaker: Tiago Sousa Mota (PHD student at IME-UFG)
Title: Convergência de um método de descida para funções que satisfazem a desigualdade de Lojasiewicz
Abstract: Nesta palestra analisaremos os resultados do trabalho: Alaa N. E. e Pierre M. intitulado "Convergência para o equilíbrio para sistemas discretizados do tipo gradiente com características analíticas". Um modelo abstrato foi proposto para minimizar uma função suave que satisfaz a propriedade de Kurdyka–Lojasiewicz, os resultados de convergência e a taxa de convergência desse modelo abstrato serão apresentados e uma análise será feita em relação ao comprimento do passo no caso em que é limitado e no caso em que é somável. Finalmente, discutiremos algumas possibilidades para trabalhos futuros.
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Date: October 17
Local: Classroom at IME-UFG
Time: 8:30 am to 9:50 am
Speaker: Paulo César (PHD student at IME-UFG)
Title: Secant-Type Methods with Feasible Inexact Projection for Solving Constrained Mixed Generalized Equations
Abstract: This presentation investigates new variants of secant-type methods to solve constrained generalized equations. Specifically, the proposed approach integrates the traditional secant method with the conditional gradient (Frank-Wolfe) method, aiming to enhance convergence properties and computational efficiency in complex constrained problems. The algorithm's convergence is established using the contraction mapping principle, while assuming Lipschitz continuity on the gradients of involved functions and employing the metric regularity property of mappings. These assumptions ensure that the generated sequence is well-defined and converges locally with a linear or superlinear rate, depending on problem-specific conditions.
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Date: October 31
Local: Classroom at IME-UFG
Time: 8:30 am to 9:50 am
Speaker: Orizon Pereira Ferreira (Professor at IME-UFG)
Title: New Properties of Busemann Function and Difference of Convex Algorithms on Hadamard Manifolds
Abstract: This presentation explores new properties of the Busemann function on Hadamard manifolds and its implications for optimization algorithms within Riemannian frameworks. We examine difference of convex (DC) optimization problems on these manifolds, focusing on the reformulation and analysis of the classic difference of convex algorithm (DCA) and the proximal DCA. These algorithms are extended from Euclidean to Riemannian settings, demonstrating their effectiveness in solving DC optimization problems in a non-Euclidean context.
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Date: November 07
Local: Classroom at IME-UFG
Time: 8:30 am to 9:50 am
Speaker: Luis Roman Lucambio Perez (Professor at IME-UFG)
Title: Exploring the relationship between scalar and vector optimization
Abstract: This talk discusses efficient ways of finding optimal solutions to convex optimization problems via vector optimization procedures.
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Date: November 14
Local: Classroom at IME-UFG
Time: 8:30 am to 9:50 am
Speaker: Tiago Sousa Mota (PHD student at IME-UFG)
Title: A Discussion on the Convergence Rate of Inexact Gradient Methods for Functions Satisfying the Łojasiewicz Inequality
Abstract: In this talk, we consider the abstract descent method proposed and developed by Khanh, Mordukhovich, and Tran (J Optim Theory Appl https://doi.org/10.1007/
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Date: November 28
Local: Classroom at IME-UFG
Time: 8:30 am to 9:50 am
Speaker: Claudemir Rodrigues Santiago (PHD student at IME-UFG)
Title: On the Convergence of a Monotone Proximal Gradient Method on Hadamard Manifolds
Abstract: In this talk, we will present some aspects of the extension of a Euclidean proximal gradient method to Hadamard manifolds, for solving
composite-type problems (i.e., the function F = f + g, where f is differentiable and g is convex). Specifically, we will prove the well-definitionand some convergence results of the proposed method without requiring the global Lipschitz continuity of the gradient of f.
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Date: December 03
Local: Auditorium at IME-UFG
Time: 9:00 am to 10:00 am
Speaker: Prof. Julien Ugon (Professor at Deakin University, Melbourne, Australia)
Title: Towards developing proximal methods for minimising abstract convex functions
Abstract: Abstract convexity is a type of generalised convexity that relies on nonlinear separation of sets. Specifically, where, classically, convex sets are those separated (from outside points) using affine functions, abstract convex sets are separated using a different family of nonlinear functions. This leads to a rich theory of particular interest for optimising nonconvex functions. In this talk I will report on results from our recent investigations of the abstract subdifferential operators, with a specific focus on establishing general calculus rules, investigating the maximal monotonicity of the operator, and ultimatly progressing towards our goal to develop algorithms based on abstract convexity.
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Date: December 03
Local: Auditorium at IME-UFG
Time: 10:30 am to 11:30 am
Speaker: Prof. Reinier Díaz Millán (Professor at Deakin University, Melbourne, Australia)
Title: Faces of convex sets and its relation with the generalised interior
Abstract: This talk explores the intrinsic core and generalised interior in the context of convex sets within topological real vector spaces. The intrinsic core generalizes the classical notion of the relative interior from finite-dimensional spaces to arbitrary real vector spaces, and we review several equivalent definitions, highlighting its connection to the facial structure of convex sets. We also introduce a new concept of face relative interior, grounded in the facial structure, which refines other generalizations of the relative interior by capturing the geometry of convex sets more effectively in topological spaces.
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Date: December 05
Local: Classroom at IME-UFG
Time: 8:00 am to 9:20 am
Speaker: Vilmar G. Filho (Master's student at IME-UFG)
Title: A cubic regularization method with lazy approximated of Hessian
Abstract: In this talk, we discuss first-order (Hessian-free) and zero-order (derivative-free) implementations of the Cubically regularized Newton method for solving general non-convex optimization problems. Complexity results for finding first- and second-order stationary points are presented.
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