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中文摘要：
对广泛应用于工程设计、非线性系统稳定性分析等实际问题中的一类线性比式和问题（P1）提出了一种鲁棒全局优化算法，这种方法求得的最优解具有稳定性好，可行等特点．从理论上证明了该算法的收敛性，最终数值实验表明了提出方法的可行性．
英文摘要：
A robust algorithm is proposed for a class of linear sum of ratios problem （P1）, which can be applied to engineering designs and stability analysis of nonlinear systems and so on pratical problems. The proposed algorithm provides a global optimal solution which is also stable under small perturbations of the constraints, and is adequately guaranteed to be feasible. From theory the proof which the proposed branch and bound algorithm is convergent to the global minimum is given. And finally the numerical experiments problem are given to illustrate the feasibility of the proposed algorithm.
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