A branch-and-bound algorithm for maximizing the sum of several linear ratios

Authors:
Takahito Kuno
Affiliations:
Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan (E-mail: takahito@is.tsukuba.ac.jp)
Venue:
Journal of Global Optimization
Year:
2002

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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.