Interior Point Methods Iteration Count Reduction Using Continued Iteration and Simple Algorithms

• Grant number: 11/20623-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: July 01, 2012
• End date: January 31, 2016
• Field of knowledge: Engineering - Production Engineering - Operational Research
• Principal Investigator: Aurelio Ribeiro Leite de Oliveira
• Grantee: Lilian Ferreira Berti
• 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. Since these techniques require a small amount of computational effort in comparison to compute a direction in a new iteration, the number of iterations reductions should be followed by a reduction in processing time.

Academic Publications

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

BERTI, Lilian Ferreira. Interior point methods iteration reduction with continued iteration. 2016. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Ciência da Computação Campinas, SP.