Development and Analysis of Ellipsoidal Methods with Applications in Non-Smooth Optimization and Equilibrium Problems

• Grant number: 25/21077-9
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2026
• End date: February 29, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Ernesto Julián Goldberg Birgin
• Grantee: Eduarda Ferreira Zanatta
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 23/08706-1 - Numerical optimization, AP.TEM

Abstract

This project focuses on the theoretical development and rigorous analysis of advanced methods in continuous optimization, with a particular emphasis on the ellipcentered method. The research is structured along three main directions: first, the extended development of the elliptic-centered method, broadening its applicability to strongly convex functions as well as to new classes of convex and potentially non-convex functions, while thoroughly investigating key properties such as global convergence, convergence rates, numerical stability, and computational complexity; second, the study of functions composed of both differentiable and non-differentiable terms, addressing challenges arising from the loss of differentiability and the need for subdifferential analysis, and exploring regularization and proximal techniques to ensure convergence; and third, the application of these methods to general equilibrium and complementarity problems, which are prevalent in fields such as economics, engineering, and game theory. This research aligns with the institution's focus areas, particularly in numerical optimization and computational modeling, and aims to enhance the researcher's expertise while fostering the development of innovative solutions with significant scientific and societal impact. (AU)