Methods in optimization and feasibility: applications in tomography

• Grant number: 08/10030-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2009
• End date: June 30, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Alvaro Rodolfo de Pierro
• Grantee: Elias Salomão Helou Neto
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In our doctoral dissertation we presented a general framework that includes many known as well as new methods for solving convex feasibility problems and for constrained nondifferentiable optimization. These methods generalize orthogonal projection methods for convex feasibility as well as underrelaxed methods for nondifferentiable convex optimization. This project aims at extending these methods in two directions: the resolution of constrained but inconsistent problems and the use of duality concepts. Another fundamental goal is the application of the methods in tomography problems, taking the new uncertainty principles as a departure point. (AU)

Scientific publications

(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)

HELOU NETO, ELIAS SALOMAO; DE PIERRO, ALVARO RODOLFO. On perturbed steepest descent methods with inexact line search for bilevel convex optimization. OPTIMIZATION, v. 60, n. 8-9, p. 18-pg., 2011-01-01. (08/10030-6)

HELOU NETO, ELIAS SALOMAO; DE PIERRO, ALVARO RODOLFO. On perturbed steepest descent methods with inexact line search for bilevel convex optimization. OPTIMIZATION, v. 60, n. 8-9, SI, p. 991-1008, 2011. (08/10030-6)