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Second-order algorithms for nonlinear optimization with strong optimality properties

Grant number: 17/12187-9
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2018
Effective date (End): February 28, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Gabriel Haeser
Grantee:Thiago Parente da Silveira
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:13/05475-7 - Computational methods in optimization, AP.TEM

Abstract

This project deals with the general nonlinear optimization problem in euclidean space with twice continuously differentiable function. Relating to second-order necessary optimality condition, there is a gap between conditions that can be proved (theoretical) and conditions that can be attained by an iterative algorithm (practical), in the sense that the theoretical ones are at the present time much stronger than the practical ones. The goal of this project is to reduce this gap, developing a practical second-order algorithm with better properties with respect to optimality. The relevance of this work is given by the practical need to develop algorithms that not only generate first-order stationary points, but also, that provide better guaranties of optimality. (AU)