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.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

GRILLO, Gabriel Rodrigues Silva. Partially smooth minimization of non-smooth functions and applications to linear inverse problems. 2024. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.