Proximal methods and regularization

• Grant number: 19/15992-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2019
• End date: 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

Abstract

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.