Partially smooth minimization of non-smooth functions and applications to linear inverse problems

• Grant number: 22/10506-8
• Support Opportunities: Scholarships in Brazil - Master
• Start date: November 01, 2022
• End date: February 29, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Sandra Augusta Santos
• Grantee: Gabriel Rodrigues Silva Grillo
• 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 establishes a roadmap for the development of numerical methods for the minimization of composite functions, which are written as the sum of two potentially non-smooth terms. The idea is to smooth the term that is unfavorable to the proximal operator, aiming to meet the hypotheses of recently proposed first-order accelerated algorithms. The designed algorithm will be accompanied by its complexity analysis. Computational experiments applied to linear inverse problems will contextualize the developed theoretical elements.