Computational optimization methods and applications with emphasis on problems with imprecise information.

• Grant number: 26/00596-0
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2026
• End date: July 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Luis Felipe Cesar da Rocha Bueno
• Grantee: Luis Felipe Cesar da Rocha Bueno
• Host Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil
• City of the host institution: São José dos Campos

Abstract

This project proposes the theoretical and computational development of optimization methods to solve problems with inexact information arising from a variety of topics that are relevant to society. We will be particularly interested in optimization problems with constraints given by differential equations. Along this line, we aim to quantify error propagation in the adjoint method, develop a convergence analysis in which the use of inexact gradients can be accommodated within general direction frameworks for classical methods, address problems that involve constraints depending on state variables (in addition to residual equations), propose algorithms in which state variables are computed as inexact functions of the control variables while the convergence theory treats them as independent variables, and validate the theory through applications in aerodynamic design. Another main line of investigation will focus on problems involving large-scale data. We intend to consolidate an Inexact Restoration method to control the level of accuracy in the evaluation of the objective function and the constraints, as well as to establish sequential optimality conditions, develop stochastic convergence analysis, and explore applications to financial credit problems. In addition to these main research directions, this project is expected to foster discussions on related topics in which the proponent is already involved. (AU)