Regularized block coordinate descent methods [resumo]: complexity and applications (2025)
- Autor:
- Autor USP: BIRGIN, ERNESTO JULIAN GOLDBERG - IME
- Unidade: IME
- Subjects: OTIMIZAÇÃO MATEMÁTICA; APRENDIZADO COMPUTACIONAL; ALGORITMOS
- Keywords: Problemas de minimização; Experimentos numéricos
- Language: Inglês
- Abstract: In this work, we propose block coordinate descent methods for bound-constrained and nonconvex constrained minimization problems. Our approach relies on solving regularized models. For bound-constrained problems, we introduce methods based on models of order p, which exhibit asymptotic convergence to pth-order stationary points. Moreover, first-order stationarity with precision E with respect to the variables of each block is achieved in O(E−(p+1)/p); while first-order stationarity with precision E with respect to all the variables is achieved in O(E−(p+1)). For nonconvex constrained minimization, we consider models with quadratic regularization. Given feasibility/complementarity and optimality tolerances δ > 0 and E > 0 for feasibility/complementarity and optimality, respectively, it is shown that a measure of (δ, 0)-criticality tends to zero; and the number of iterations and functional evaluations required to achieve (δ, E)-criticality is O(E−2). Numerical experiments illustrate the effectiveness of our methods. We apply the first method to solve the Molecular Distance Geometry Problem, while the second method is used to enhance heuristic approaches for the Traveling Salesman Problem (TSP) with neighbors, a variant of the classical TSP problem where regions in the plane must be visited instead of cities. The case where regions are described by arbitrary (nonconvex) polygons is considered.
- Imprenta:
- Publisher: Fundação Getulio Vargas FGV
- Publisher place: Rio de Janeiro
- Date published: 2025
- Source:
- Título: Book of Abstracts
- Volume/Número/Paginação/Ano: p. 3, 2025
- Conference titles: Carioca Workshop on Optimization and Applications - CariOPT
-
ABNT
BIRGIN, Ernesto Julian Goldberg. Regularized block coordinate descent methods [resumo]: complexity and applications. 2025, Anais.. Rio de Janeiro: Fundação Getulio Vargas FGV, 2025. p. 3. Disponível em: https://drive.google.com/file/d/1IMnaoGpl1jeiG5dhzmGoqnTIaQZBCRYo/view?usp=sharing. Acesso em: 09 fev. 2026. -
APA
Birgin, E. J. G. (2025). Regularized block coordinate descent methods [resumo]: complexity and applications. In Book of Abstracts (p. 3). Rio de Janeiro: Fundação Getulio Vargas FGV. Recuperado de https://drive.google.com/file/d/1IMnaoGpl1jeiG5dhzmGoqnTIaQZBCRYo/view?usp=sharing -
NLM
Birgin EJG. Regularized block coordinate descent methods [resumo]: complexity and applications [Internet]. Book of Abstracts. 2025 ; 3.[citado 2026 fev. 09 ] Available from: https://drive.google.com/file/d/1IMnaoGpl1jeiG5dhzmGoqnTIaQZBCRYo/view?usp=sharing -
Vancouver
Birgin EJG. Regularized block coordinate descent methods [resumo]: complexity and applications [Internet]. Book of Abstracts. 2025 ; 3.[citado 2026 fev. 09 ] Available from: https://drive.google.com/file/d/1IMnaoGpl1jeiG5dhzmGoqnTIaQZBCRYo/view?usp=sharing - An augmented Lagrangian method with finite termination
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