On the convergence of interior point methods combined with continued iteration and simple algorithms

• Grant number: 13/02089-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2013
• End date: February 02, 2016
• Field of knowledge: Engineering - Production Engineering - Operational Research
• Principal Investigator: Aurelio Ribeiro Leite de Oliveira
• Grantee: Luciana Yoshie Tsuchiya
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 10/06822-4 - Efficient solution of large-scale linear and quadratic programming problems, AP.TEM

Abstract

The simple linear programming algorithms have appeared from the generalization of Von Neumann ideas. The main advantage of such algorithms is the simplicity, that is, in each iteration, it is only needed to perform matrix vector multiplications and solve positive definite linear systems of small dimension, On the other hand, the continued iteration consists in projecting the search direction in such a way that the blocking variable has a null direction. The combination of both approaches is used aiming to reduce the total number of interior point methods iterations and the total processing time. This research project aims to study the interior point methods convergence properties when combined with the techniques proposed above.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

TSUCHIYA, Luciana Yoshie. Incomplete Cholesky factorizations for the direct solution of linear systems arising from interior point methods. 2017. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.