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Proximal methods and regularization

Grant number: 19/15992-5
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): September 01, 2019
Effective date (End): February 28, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:Sandra Augusta Santos
Grantee:Gabriel Passos
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:18/24293-0 - Computational methods in optimization, AP.TEM


This project outlines a roadmap of theoretical studies for the proximal point methods. It starts from the basic notions of convexity, duality and regularization, prerequisites for the understanding of the proximal operators and their main properties. The new information and concepts will be organized in the form of a glossary. The written language, interconnections with topics already studied along the undergraduate courses, and the organization of ideas will permeate the whole study, culminating in the analysis of convergence properties of the ADMM algorithm, and its applications to structured problems.

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