Ellipsoid packing

• Grant number: 12/23916-8
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2013
• End date: August 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Ernesto Julián Goldberg Birgin
• Grantee: Rafael Durbano Lobato
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The sphere-packing problem has been the subject of intense theoretical and experimental research. The problem of packing ellipsoids, on the other hand, began to receive attention only very recently and has applications in many areas. In particular, this problem has important applications in the formation and growth of crystals, the structure of liquids, crystals and glasses, the flow and compression of granular materials and glasses, and the thermodynamics and kinetics of the liquid to crystal transition. The problem of packing ellipsoids also finds applications in the organization of chromosomes in human cell nuclei. In this project, we intend to develop nonlinear programming models and algorithms for the packing of ellipsoids. (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)

BIRGIN, E. G.; LOBATO, R. D.; MARTINEZ, J. M.. A nonlinear programming model with implicit variables for packing ellipsoids. Journal of Global Optimization, v. 68, n. 3, p. 467-499, JUL 2017. (13/07375-0, 13/05475-7, 10/10133-0, 13/03447-6, 12/23916-8)

BIRGIN, E. G.; LOBATO, R. D.. A matheuristic approach with nonlinear subproblems for large-scale packing of ellipsoids. European Journal of Operational Research, v. 272, n. 2, p. 447-464, JAN 16 2019. (13/07375-0, 17/05198-4, 16/01860-1, 13/05475-7, 15/18053-9, 13/03447-6, 12/23916-8)

MARTIN, MATEUS; BIRGIN, ERNESTO G.; LOBATO, RAFAEL D.; MORABITO, REINALDO; MUNARI, PEDRO. Models for the two-dimensional rectangular single large placement problem with guillotine cuts and constrained pattern. International Transactions in Operational Research, v. 27, n. 2, JULY 2019. (13/07375-0, 16/01860-1, 12/23916-8, 16/08039-1)

BIRGIN, E. G.; LOBATO, R. D.; MARTINEZ, J. M.. Packing ellipsoids by nonlinear optimization. Journal of Global Optimization, v. 65, n. 4, p. 709-743, AUG 2016. (13/07375-0, 13/05475-7, 10/10133-0, 13/03447-6, 12/23916-8)

Academic Publications

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

LOBATO, Rafael Durbano. Ellipsoid packing. 2015. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.