Name
Abstract | ||
|---|---|---|
We consider the problem of optimally covering plane domains by a given number of circles. The mathematical modeling of this problem leads to a min-max-min formulation which, in addition to its intrinsic multi-level nature, has the significant characteristic of being non-differentiable. In order to overcome these difficulties, we have developed a smoothing strategy using a special class C-infinity smoothing function. The final solution is obtained by solving a sequence of differentiable subproblems which gradually approach the original problem. The use of this technique, called Hyperbolic Smoothing, allows the main difficulties presented by the original problem to be overcome. A simplified algorithm containing only the essential of the method is presented. For the purpose of illustrating both the actual working and the potentialities of the method, a set of computational results is presented. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1007/s10898-004-0737-8 | JOURNAL OF GLOBAL OPTIMIZATION |
Keywords | Field | DocType |
location problems,min-max-min problems,non-differentiable programming,smoothing | Mathematical optimization,Differentiable function,Smoothing,Mathematics | Journal |
Volume | Issue | ISSN |
31.0 | 3 | 0925-5001 |
Citations | PageRank | References |
9 | 0.68 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Adilson Xavier | 1 | 45 | 6.28 |
| Antonio Alberto Fernandes de Oliveira | 2 | 13 | 1.47 |