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On the second-order information in nonlinear optimization

Grant number: 16/02092-8
Support type:Scholarships abroad - Research
Effective date (Start): September 01, 2016
Effective date (End): August 31, 2017
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Gabriel Haeser
Grantee:Gabriel Haeser
Host: Yinyu Ye
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Local de pesquisa : Stanford University, United States  
Associated research grant:13/05475-7 - Computational methods in optimization, AP.TEM


With automatic differentiation, the second-order information of an optimization problem is frequently available for an algorithm seeking its solution. In previous works of the author and his collaborators, we have been interested in identifying first and second order properties of a local minimizer of a general nonlinear optimization problem. Our main interest has been in conditions that can be verified by a practical algorithm. In this project we will continue the research on this topic, in particular, generalizing this kind of approach to other classes of optimization problems and studying in more details the second order optimality conditions, both the classic ones and the ones associated to algorithms. We will also approach the use of negative curvature directions in optimization algorithms, as well as other topics related to the second-order information. (AU)

Scientific publications (6)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
HAESER, GABRIEL; LIU, HONGCHENG; YE, YINYU. Optimality condition and complexity analysis for linearly-constrained optimization without differentiability on the boundary. MATHEMATICAL PROGRAMMING, v. 178, n. 1-2, p. 263-299, NOV 2019. Web of Science Citations: 1.
HAESER, GABRIEL. A second-order optimality condition with first- and second-order complementarity associated with global convergence of algorithms. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 70, n. 2, p. 615-639, JUN 2018. Web of Science Citations: 2.
HAESER, G. Some theoretical limitations of second-order algorithms for smooth constrained optimization. OPERATIONS RESEARCH LETTERS, v. 46, n. 3, p. 295-299, MAY 2018. Web of Science Citations: 1.
BEHLING, ROGER; HAESER, GABRIEL; RAMOS, ALBERTO; VIANA, DAIANA S. On a Conjecture in Second-Order Optimality Conditions. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 176, n. 3, p. 625-633, MAR 2018. Web of Science Citations: 3.
BIRGIN, E. G.; HAESER, G.; RAMOS, A. Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 69, n. 1, p. 51-75, JAN 2018. Web of Science Citations: 10.
HAESER, GABRIEL. An Extension of Yuan's Lemma and Its Applications in Optimization. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, v. 174, n. 3, p. 641-649, SEP 2017. Web of Science Citations: 3.

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