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)

Scientific publications

(7)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

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. (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, MAY 2018. (16/02092-8, 13/05475-7)

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. (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, MAR 2021. (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, NOV 2019. (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, JAN 2018. (13/07375-0, 16/02092-8, 16/01860-1, 13/05475-7, 13/03447-6)

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. (16/02092-8, 13/05475-7)