Theoretical and computational issues for the efficient implementation of linear optimization methods

• Grant number: 08/09040-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2009
• End date: January 31, 2013
• Field of knowledge: Engineering - Production Engineering - Operational Research
• Principal Investigator: Marcos Nereu Arenales
• Grantee: Pedro Augusto Munari Junior
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 06/03496-3 - Theory and practice of cutting and packing problems, AP.TEM
• Associated scholarship(s): 12/05486-6 - Using the primal-dual interior point algorithm within the branch-price-and-cut method, BE.EP.DR

Abstract

The current main methods of linear optimization are the simplex-type methods and the interior-point methods. The search for techniques that can result in efficient implementations is very active and make possible solving larger and more complex problems. The purpose of this project is to develop some techniques in order to improve the efficiency of those linear optimization methods. In simplex-type methods, the goal is to explore characteristics of problems in the general form and to specialize the piecewise-linear dual simplex method in this context. In interior-point methods will be investigated the warm-start procedure for this class of methods, with important developments in the technique of column generation and in solving problems of integer optimization, where a sequence of linear optimization problems have to be solved. (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)

MUNARI, PEDRO; GONDZIO, JACEK. Using the primal-dual interior point algorithm within the branch-price-and-cut method. Computers & Operations Research, v. 40, n. 8, p. 2026-2036, AUG 2013. (12/05486-6, 08/09040-7)

Academic Publications

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

MUNARI JUNIOR, Pedro Augusto. Theoretical and computational issues for improving the performance of linear optimization methods. 2013. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.