How to divide a territory? A new simple differential formalism for optimization of set functions
✍ Scribed by Hung T. Nguyen; Vladik Kreinovich
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 194 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0884-8173
No coin nor oath required. For personal study only.
✦ Synopsis
In many practical problems, we must optimize a set function, i.e., find a set A for which Ž . f A ª max, where f is a function defined on the class of sets. Such problems appear in design, in image processing, in game theory, etc. Most optimization problems can be Ž . solved or at least simplified by using the fact that small deviations from an optimal solution can only decrease the value of the objective function; as a result, some derivative must be equal to 0. This approach has been successfully used, e.g., for set functions in Ž . which the desired set A is a shape, i.e., a smooth or piece-wise smooth surface. In some real-life problems, in particular, in the territorial division problem, the existing methods are not directly applicable. For such problems, we design a new simple differential formalism for optimizing set functions.