Scholarship 16/02092-8 - Otimização matemática, Algoritmos - BV FAPESP
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On the second-order information in nonlinear optimization

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

Abstract

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)

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Scientific publications (7)
(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)
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, . (16/02092-8, 13/05475-7)
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, . (16/02092-8, 13/05475-7)
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, . (13/07375-0, 16/02092-8, 16/01860-1, 13/05475-7, 13/03447-6)
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, . (16/02092-8, 13/05475-7)
HAESER, GABRIEL; HINDER, OLIVER; YE, YINYU. On the behavior of Lagrange multipliers in convex and nonconvex infeasible interior point methods. MATHEMATICAL PROGRAMMING, v. 186, n. 1-2, p. 257-288, . (16/02092-8, 13/05475-7)
HAESER, G.. Some theoretical limitations of second-order algorithms for smooth constrained optimization. OPERATIONS RESEARCH LETTERS, v. 46, n. 3, p. 295-299, . (16/02092-8, 13/05475-7)
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, . (16/02092-8, 13/05475-7)

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