• 论文 •

### 线性比式和规划问题的输出空间分支定界算法

1. 1. 北方民族大学数学与信息科学学院, 银川 750021;
2. 宁夏科学计算与智能信息处理协同创新中心, 银川 750021;
3. 宁夏大学数学统计学院, 银川 750021
• 收稿日期:2018-07-25 出版日期:2020-05-15 发布日期:2020-05-15
• 基金资助:

国家自然科学基金（11961001），宁夏高等教育一流学科建设资助项目（NXYLXK2017B09），北方民族大学重大专项（ZDZX201901）资助.

Gao YueLin, Zhang Bo. AN OUTCOME-SPACE BRANCH AND BOUND ALGORITHM FOR THE SUM-OF-LINEAR-RATIOS PROGRAMMING PROBLEM[J]. Mathematica Numerica Sinica, 2020, 42(2): 207-222.

### AN OUTCOME-SPACE BRANCH AND BOUND ALGORITHM FOR THE SUM-OF-LINEAR-RATIOS PROGRAMMING PROBLEM

Gao YueLin1,2, Zhang Bo2,3

1. 1. School of mathematics and information science, North Minzu University, Yinchuan 750021, China;
2. Ningxia province cooperative innovation center of scientific computing and intelligent information processing, Yinchuan 750021, China;
3. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
• Received:2018-07-25 Online:2020-05-15 Published:2020-05-15

In this paper, a new global optimization algorithm is proposed for a class of NP-hard nonlinear programming problems: the sum-of-linear-ratios Programming problem. First of all, the original problem is equivalent to a nonlinear programming problem by introducing p auxiliary variables, and the objective function of the nonlinear programming problem is the sum of the product. At the same time, p new nonlinear equality constraints are added to the original problem. By constructing convex and concave envelopes, the objective function and constraint conditions of the equivalent problem are reduced linearly to form a lower bound linear relaxation programming problem of the original problem. A branch and bound algorithm based on solving the linear programming problem is proposed, and the convergence of the algorithm is proved. Finally, the numerical results show that the proposed algorithm is feasible and effective.

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