Global Optimization for a Class of Nonlinear Sum of Ratios Problem

We present a branch and bound algorithm for globally solving the sum of ratios problem. In this problem, each term in the objective function is a ratio of two functions which are the sums of the absolute values of affine functions with coefficients. This problem has an important application in finan...

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Bibliographic Details
Published in:Mathematical problems in engineering 2014-01, Vol.2014 (1)
Main Authors: Jin, Li, Hou, Xue-Ping
Format: Article
Language:English
Subjects:
Algorithms
Branch and bound methods
Convergence
Global optimization
Heuristic
Mathematical analysis
Mathematical models
Mathematical problems
Nonlinearity
Optimization
Partitioning
Ratios
Searching
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Summary:We present a branch and bound algorithm for globally solving the sum of ratios problem. In this problem, each term in the objective function is a ratio of two functions which are the sums of the absolute values of affine functions with coefficients. This problem has an important application in financial optimization, but the global optimization algorithm for this problem is still rare in the literature so far. In the algorithm we presented, the branch and bound search undertaken by the algorithm uses rectangular partitioning and takes place in a space which typically has a much smaller dimension than the space to which the decision variables of this problem belong. Convergence of the algorithm is shown. At last, some numerical examples are given to vindicate our conclusions.
ISSN:1024-123X
1563-5147
DOI:10.1155/2014/103569