Global Optimization for a Class of Nonlinear Sum of Ratios Problem | Zendy

Li Jin | Zendy; Xue-Ping Hou | Zendy

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Global Optimization for a Class of Nonlinear Sum of Ratios Problem

Author(s) -

Li Jin,

Xue-Ping Hou

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/103569

Subject(s) - dimension (graph theory) , mathematics , optimization problem , convergence (economics) , mathematical optimization , space (punctuation) , global optimization , affine transformation , branch and bound , class (philosophy) , function (biology) , upper and lower bounds , nonlinear system , term (time) , computer science , combinatorics , pure mathematics , mathematical analysis , physics , quantum mechanics , artificial intelligence , evolutionary biology , economics , biology , economic growth , operating system

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

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