Methods for nonlinear programming with evaluation complexity results

• Grant number: 17/03504-0
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): September 01, 2017
• Effective date (End): January 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal researcher: Sandra Augusta Santos
• Grantee: John Lenon Cardoso Gardenghi
• Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 13/05475-7 - Computational methods in optimization, AP.TEM

Abstract

In the present project, we are interested in studying and developing an implementation for the algorithm proposed in E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos e Ph. L. Toint. Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models, SIAM Journal on Optimization, 26(2), 951-967, 2016. Although this method possesses good theoretical properties of convergence and evaluation complexity, it may present a poor practical numerical performance, possibly by taking tiny steps far from the solution. Therefore, we plan to investigate these potential drawbacks and to detect the circumstances under which such deficiencies are irrelevant. We aim to achieve a software able to solve nonlinear programming problems with the proposed algorithm, beyond numerical experiments with classical problems from literature. (AU)