Constraint qualifications for conic optimization

• Grant number: 25/11363-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2025
• End date: September 30, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Ernesto Julián Goldberg Birgin
• Grantee: Hilal Ahmad Bhat
• 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

In this project, we aim to build upon recent developments in this area by addressing several open questions. In particular, a reduction strategy was recently introduced to handle situations in which the constraint does not lie at the vertex of the cone. In this project, we intend to propose a reduction-free condition to formulate the optimality condition. Furthermore, we aim to investigate all known applications of the constant rank condition in the context of nonlinear programming and explore their extensions to more general conic optimization settings, such as its use in the computation of the value function derivative and its application to algorithmic convergence. Settings on Riemannian manifolds will also be considered. (AU)