A branch-and-bound algorithm for maximizing the sum of several linear ratios |
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Authors: | Takahito Kuno |
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Institution: | (1) Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, Ibaraki, 305-8573, Japan |
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Abstract: | In this paper, we develop a branch-and-bound algorithm for maximizing a sum of p (slant2) linear ratios on a polytope. The problem is embedded into a 2p-dimensional space, in which a concave polyhedral function overestimating the optimal value is constructed for the bounding operation. The branching operation is carried out in a p-dimensional space, in a way similar to the usual rectangular branch-and-bound method. We discuss the convergence properties and report some computational results. |
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