| Full text | |
| Author(s): |
Birgin, E. G.
;
Laurain, A.
;
Menezes, T. C.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Mathematics of Computation; v. 92, n. 344, p. 54-pg., 2023-05-12. |
| Abstract | |
. Minimization diagrams encompass a large class of diagrams of interest in the literature, such as generalized Voronoi diagrams. We develop an abstract perturbation theory in two dimensions and perform a sensitivity analysis for functions depending on sets defined through intersections of smooth sublevel sets, and formulate precise conditions to avoid singular situations. This allows us to define a general framework for solving optimization problems depending on two-dimensional minimization diagrams. The particular case of Voronoi diagrams is discussed to illustrate the general theory. A variety of numerical experiments is presented. The experiments include constructing Voronoi diagrams with cells of equal size, cells satisfying conditions on the relative size of their edges or their internal angles, cells with the midpoints of pairs of Voronoi and Delaunay edges as close as possible, or cells of varying sizes governed by a given function. Overall, the experiments show that the proposed methodology allows the construction of customized Voronoi diagrams using off-the-shelf well-established optimization algorithms. (AU) | |
| FAPESP's process: | 18/24293-0 - Computational methods in optimization |
| Grantee: | Sandra Augusta Santos |
| Support Opportunities: | Research Projects - Thematic Grants |
| 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: | 21/05168-3 - A continuous optimization approach to the tessellation generation problem |
| Grantee: | Tiago da Costa Menezes |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 16/01860-1 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings |
| Grantee: | Reinaldo Morabito Neto |
| Support Opportunities: | Research Projects - Thematic Grants |