Maximization of the Choquet integral over a convex set and its application to resource allocation problems

Mikhail Timonin ()

Annals of Operations Research, 2012, vol. 196, issue 1, 543-579

Abstract: We study the problem of the Choquet integral maximization over a convex set. The problem is shown to be generally non-convex (and non-differentiable). We analyze the problem structure, and propose local and global search algorithms. The special case when the problem becomes concave is analyzed separately. For the non-convex case we propose a decomposition scheme which allows to reduce a non-convex problem to several concave ones. Decomposition is performed by finding the coarsest partition of a capacity into disjunction of totally monotone measures. We discuss its effectiveness and prove that the scheme is optimal for 2-additive capacities. An application of the developed methods to resource allocation problems concludes the article. Copyright Springer Science+Business Media, LLC 2012

Keywords: Multicriteria decision making; Resource allocation; Choquet integral; Optimization (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10479-012-1147-9

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