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Global optimization for sum of linear ratios problem with coefficients. (English) Zbl 1098.65066
The following nonconvex optimization problem is considered: \[ \max f(x)\equiv \sum^m_{i=1}c_in_i(x)/d_i(x)\text{ subject to }x\in X\equiv\{x|Ax\leq b\}y, \] where \(m\geq 2\), \(n_i(x)\geq 0\), \(d_i(x)>0\) are for all \(x\in X\) affine functions on \(\mathbb R^n\), and \(c_i\) are constant coefficients, \(i=1,\dots,m\). The problem has applications e.g., in transportation planning, finance and investment, government planning, and other areas. A branch and bound algorithm for finding the global optimal solution of the problem is proposed, its convergence is proved, and its numerical effectiveness is demonstrated on smaller numerical examples with \(n=3\).

MSC:
65K05 Numerical mathematical programming methods
90C26 Nonconvex programming, global optimization
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