Optimal Covering of Plane Domains by Circles Via Hyperbolic Smoothing
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 o...
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| Veröffentlicht in: | Journal of global optimization 2005-03, Vol.31 (3), p.493-504 |
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| container_title | Journal of global optimization |
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| creator | Xavier, Adilson Elias Oliveira, Antonio Alberto Fernandes De |
| description | 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 ? 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. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1007/s10898-004-0737-8 |
| format | Article |
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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 ? 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. 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| title | Optimal Covering of Plane Domains by Circles Via Hyperbolic Smoothing |
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