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A nonlinear optimization approach to the covering problem

Grant number: 19/25258-7
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): February 01, 2020
Effective date (End): May 05, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal researcher:Ernesto Julián Goldberg Birgin
Grantee:Rafael Massambone de Oliveira
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:18/24293-0 - Computational methods in optimization, AP.TEM

Abstract

In this project we intend to address a complementary problem to the packing problem. This is the covering problem. In the covering problem that we want to study, given a region of the n-dimensional space and a fixed amount N of identical and variable sized items, we want to find the minimum dimension that the items must have to cover the object. A concrete example is to find the configuration (position of the centers) and the radius that N identical circles must have to cover a unit-side square. Problems of this kind have been solved geometrically. Another option already studied is to replace the object to be covered by a finite set of points. In this project we intend to study the possibility of formulating the problem as a continuous optimization problem and try to solve it with classical techniques of continuous optimization. (AU)

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