Integration of Continuous and Discrete Optimization Methods in the Distance Geometry Problem with Data Uncertainties

• Grant number: 24/15980-5
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: January 12, 2025
• End date: July 16, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Roberto Andreani
• Grantee: Mariana da Rosa
• Supervisor: Marcos Raydan
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Universidade Nova de Lisboa, Portugal
• Associated to the scholarship: 22/06745-7 - Augmented Lagrangian methods for constrained optimization using differentiable exact penalty, BP.DR

Abstract

This research internship project abroad, to be conducted at the NOVA University of Lisbon under the supervision of Prof. Marcos Raydan, aims to enhance the study of the Distance Geometry problem with uncertainties. By utilizing an approach that integrates continuous and discrete optimization techniques, the main objective is to develop more efficient and robust methods to solve complex problems, such as the determination of three-dimensional protein structures. The internship will allow for the consolidation and refinement of a first version of the method that combines alternating projection, spectral gradient, and combinatorial techniques, such as Branch-and-Prune. Additionally, the project seeks to establish a solid theoretical foundation to ensure the convergence of the developed methods.