Theory and implementation of augmented Lagrangian methods with complexity guarantees for black-box problems.

• Grant number: 25/21743-9
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: April 01, 2026
• End date: March 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Ernesto Julián Goldberg Birgin
• Grantee: Diaulas Murize Santana Vieira Marcondes
• Supervisor: Geovani Nunes Grapiglia
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Universitè Catolique de Louvain (UCL), Belgium
• Associated to the scholarship: 24/22384-0 - Implementation of augmented Lagrangian methods with first-order information, BP.PD

Abstract

Nonlinear constrained optimization problems arise recurrently in large-scale modern applications such as machine learning, telecommunications, financial markets, among others. In many of these contexts, derivatives of the functions involved are not available or their computation is expensive, which limits the application of traditional methods based on gradients and Hessians. In this scenario, derivative-free approaches emerge as viable alternatives for solving these problems. Algencan is a modern and efficient augmented Lagrangian method for large-scale problems, but its derivative-free version has not yet been explored with theoretical complexity guarantees. The goal of this project is to investigate, develop, and implement a derivative-free version of Algencan. This version will incorporate a theoretical foundation with convergence guarantees and worst-case complexity results. It will also include an implementation capable of handling large-scale problems. The computational performance of the implementation will be evaluated with numerical experiments. As a result, we expect to obtain a method of augmented Lagrangians for black-box problems with constraints that has a theoretical foundation.