## 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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### References:

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