Sequential optimality conditions for nonlinear symmetric cone programming

• Grant number: 21/04979-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: July 01, 2021
• End date: September 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Gabriel Haeser
• Grantee: Lucas dos Santos Fernandez
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 18/24293-0 - Computational methods in optimization, AP.TEM

Abstract

This research project aims to extend the approximate KKT sequential condition for the context of nonlinear symmetric cone programming. For this purpose, an appropriate definition of the optimality condition is necessary so that it holds in a local minimizer without the need to require a qualification condition. In addition, such a condition must be satisfied by limit points of algorithms in this context. The strength of the condition must also be investigated. Therefore, it is expected to obtain convergence theorems for stationary points under weaker hypotheses than the usual ones. (AU)