Inexact Restoration in Stochastic Optimization

• Grant number: 25/01919-5
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: May 15, 2025
• End date: November 14, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Luis Felipe Cesar da Rocha Bueno
• Grantee: Matheus Fideles Leite
• Supervisor: Stefania Bellavia
• Host Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil
• Institution abroad: Università degli Studi di Firenze, Italy
• Associated to the scholarship: 24/03354-2 - Inexact Restoration for Inaccurate Optimization Problems, BP.MS

Abstract

Inexact Restoration (IR) is a widely known and applied approach in optimization, withwell-established methods for constrained deterministic problems. Many of the contribu-tions in this field were made by the group to which the advisor of this project belongs.However, the application of IR to stochastic optimization has been adapted to uncon-strained cases by the research group of the host supervisor of this project. Moreover, theyare currently working on extending an unconstrained finite-sum minimization algorithmto constrained stochastic problems, with collaboration with the candidate adviser. Wepropose that in this internship the candidate studies the theory of stochastic methods, animportant topic that is not yet fully mastered by the Brazilian group. We hope the can-didate becomes familiar with both the unconstrained case and the ongoing developmentof the constrained method. The student is also expected to engage with computationalimplementations of the developed algorithms and to explore options for regularizationtechniques and line search in the stochastic context.