Constraint qualifications for conic optimization

• Grant number: 24/21317-7
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: March 01, 2025
• End date: July 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Gabriel Haeser
• Grantee: Matias Oliveira Schwarz
• 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

Recent developments in the field of conic optimization have addressed various open questions. In particular, a reduction strategy was employed to handle situations where the constraint is not located at the vertex of the cone. In this project, we aim to propose a reduction-free manner to formulate this condition. Additionally, we intend to investigate all known applications of constant rank in the context of classical optimization and extend them to more general conic optimization settings, such as their utility in calculating the derivative of the value function as well as their application to algorithm convergence.