Matrix completion problems and applications

• Grant number: 25/22123-4
• Support Opportunities: Scholarships abroad - Research
• Start date: August 01, 2026
• End date: July 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Gabriel Haeser
• Grantee: Gabriel Haeser
• Host Investigator: Henry Wolkowicz
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: University of Waterloo, Canada
• Associated research grant: 23/08706-1 - Numerical Optimization, AP.TEM

Abstract

In many practical situations, data regarding a specific problem are collected in matrix form. Such data often contain errors, unknown entries, or information that is difficult to obtain. The matrix completion problem consists in completing or approximating the collected matrix by a structured matrix, that is, one with certain desired properties. In this project, we propose the study of the problem of completing a matrix with prescribed eigenvalues, which has various applications in chemistry and other fields. The intermediate steps include the development of a Newton method on manifolds and the refinement of a facial reduction procedure for nonlinear conic problems.