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Abstract: In many practical problems, we must optimize a set function, i.e., find a set A for which f(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 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... (Update)
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.... techniques for solving discrete optimization problems (which are usually difficult to solve NP hard, to be more precise) ffl In [5], it is shown how a similar discrete derivative can help to optimize functions of sets, i.e. functions f(t) in which the variable t can...
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BibTeX entry: (Update)
H. T. Nguyen and V. Kreinovich, "How to Divide a Territory? A New Simple Differential Formalism for Optimization of Set Functions", International Journal of Intelligent Systems, 1999, Vol. 14, No. 3, pp. 223--251. http://citeseer.ist.psu.edu/nguyen99how.html More
@misc{ nguyen99how,
author = "H. Nguyen and V. Kreinovich",
title = "How to Divide a Territory? A New Simple Differential Formalism for Optimization
of Set Functions",
text = "H. T. Nguyen and V. Kreinovich, How to Divide a Territory? A New Simple
Differential Formalism for Optimization of Set Functions, International
Journal of Intelligent Systems, 1999, Vol. 14, No. 3, pp. 223--251.",
year = "1999",
url = "citeseer.ist.psu.edu/nguyen99how.html" }
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