Sequential constraint qualifications for conic optimization

• Grant number: 25/27776-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2026
• End date: February 28, 2030
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Ernesto Julián Goldberg Birgin
• Grantee: Thales Brito de Souza Fonseca Rodrigues
• 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

The sequential definitions of the constant rank condition were initially developed for the second-order cone and later extended to the semidefinite cone. We propose to study a general and unified definition for general conic programming. In addition, the standard nondegeneracy condition can be made equivalent to weak nondegeneracy through the imposition of an additional linear independence condition for second-order cones, and preliminary results indicate that a similar characterization can be obtained for semidefinite cones, motivating the study of a general formulation of this type. The relationships among the various notions of weak nondegeneracy are still not fully understood, even in the simplest cases, which justifies a detailed investigation into how these conditions are related. Finally, sequential constraint qualifications can be employed in the analysis of the global convergence of algorithms, and we propose to apply these new concepts to the development and improvement of methods for general conic programming, as well as to explore other applications, such as the establishment of error bound conditions and related results. (AU)