Efficient solution of large-scale linear and quadratic programming problems

• Grant number: 10/06822-4
• Support Opportunities: Research Projects - Thematic Grants
• Start date: October 01, 2011
• End date: September 30, 2016
• Field of knowledge: Engineering - Production Engineering - Operational Research
• Principal Investigator: Aurelio Ribeiro Leite de Oliveira
• Grantee: Aurelio Ribeiro Leite de Oliveira
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Pesquisadores principais: Christiano Lyra Filho ; Secundino Soares Filho
• Associated researchers: Anesio dos Santos Junior ; Anibal Tavares de Azevedo ; Carla Taviane Lucke da Silva Ghidini ; Clovis Perin Filho ; Cristiano Torezzan ; Daniela Renata Cantane ; Fernando Rocha Villas Bôas ; Frederico Ferreira Campos Filho ; Jair da Silva ; Lilian Milena Ramos Carvalho ; Magda da Silva Peixoto ; Marcos Nereu Arenales ; Maria de Los Angeles Gonzalez Lima ; Marta Ines Velazco Fontova
• Associated research grant(s): 13/05874-9 - 26th European Conference Operational Research, AR.EXT
• Associated scholarship(s): 15/09850-2 - Operations research application to investment economic analysis, BP.IC; 13/27015-8 - Interior point methods applied to a hydroelectric system pre-dispatch with security constraints and network topology change, BP.MS; 13/02089-9 - On the convergence of interior point methods combined with continued iteration and simple algorithms, BP.DR; 11/20623-7 - Interior Point Methods Iteration Count Reduction Using Continued Iteration and Simple Algorithms, BP.DR

Abstract

Since the emergence of the interior point methods for linear optimization, computational codes based on these ideas have been shown as efficient alternatives for solving problems of linear and quadratic large-scale problems. Three research lines stand out in the search of efficiency: reducing the number of iterations to achieve convergence of the method; reduction of iteration computational time through the efficient solution of linear systems needed to compute the directions; the development of specific methods for optimization problems with particular structure and take advantage of this structure. These three lines of research are covered in this project. In the first two, the focus is linear optimization problems while quadratic programming problems on the third line originated from power systems form the core of the research. (AU)

Scientific publications

(4)

(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)

VELAZCO, MARTA; OLIVEIRA, AURELIO R. L.; KLIEWER, N; EHMKE, JF; BORNDORFER, R. Computing the Splitting Preconditioner for Interior Point Method Using an Incomplete Factorization Approach. OPERATIONS RESEARCH PROCEEDINGS 2017, v. N/A, p. 7-pg., 2018-01-01. (10/06822-4)

PEIXOTO, M. S.; CARVALHO, S. M. S.; BARROS, L. C.; BASSANEZI, R. C.; LAUREANO, E. E.; LODWICK, W. A.; LIU, J; LU, J; XU, Y; MARTINEZ, L; et al. A control to soybean aphid via fuzzy linear programming. DATA SCIENCE AND KNOWLEDGE ENGINEERING FOR SENSING DECISION SUPPORT, v. 11, p. 6-pg., 2018-01-01. (13/24148-7, 16/04299-9, 10/06822-4)

SANTOS, LUIZ-RAFAEL; VILLAS-BOAS, FERNANDO; OLIVEIRA, AURELIO R. L.; PERIN, CLOVIS. Optimized choice of parameters in interior-point methods for linear programming. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 73, n. 2, p. 535-574, JUN 2019. (08/09685-8, 10/06822-4)

PORFIRIO SUÑAGUA; AURELIO RIBEIRO LEITE OLIVEIRA. A CONSTRUCTIVE GLOBAL CONVERGENCE OF THE MIXED BARRIER-PENALTY METHOD FOR MATHEMATICAL OPTIMIZATION PROBLEMS. Pesquisa Operacional, v. 40, 2020-05-18. (10/06822-4)