Packing ellipsoids by nonlinear optimization

Author(s)

Birgin, E. G. ; Lobato, R. D. ; Martinez, J. M.

• Document type: Journal article
• Source: Journal of Global Optimization; v. 65, n. 4, p. 709-743, AUG 2016.
• Web of Science Citations: 7

Abstract

In this paper, continuous and differentiable nonlinear programming models and algorithms for packing ellipsoids in the n-dimensional space are introduced. Two different models for the non-overlapping and models for the inclusion of ellipsoids within half-spaces and ellipsoids are presented. By applying a simple multi-start strategy combined with a clever choice of starting guesses and a nonlinear programming local solver, illustrative numerical experiments are presented. (AU)

• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 13/05475-7 - Computational methods in optimization
• Grantee: Sandra Augusta Santos
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 10/10133-0 - Cutting, packing, lot-sizing and scheduling problems and their integration in industrial and logistics settings
• Grantee: Reinaldo Morabito Neto
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science
• Grantee: Carlos Eduardo Ferreira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 12/23916-8 - Ellipsoid packing
• Grantee: Rafael Durbano Lobato
• Support Opportunities: Scholarships in Brazil - Doctorate