• 论文 •

### 一类线性乘积规划问题的分支定界缩减方法

1. 1. 北方民族大学 信息与系统科学研究所, 银川 750021;
2. 宁夏大学 数学计算机学院, 银川 750021;
3. 宁夏大学 数学计算机学院, 银川 750021
• 收稿日期:2012-09-11 出版日期:2013-02-15 发布日期:2013-01-22
• 基金资助:

国家自然科学基金项目(11161001)资助.

Gao Yuelin, Jing Xia. A BRANCH-AND-BOUND REDUCED ALGORITHM FOR SOLVING A CLASS OF LINEAR MULTIPLICATIVE PROGRAMMING PROBLEMS[J]. Mathematica Numerica Sinica, 2013, 35(1): 89-98.

### A BRANCH-AND-BOUND REDUCED ALGORITHM FOR SOLVING A CLASS OF LINEAR MULTIPLICATIVE PROGRAMMING PROBLEMS

Gao Yuelin1,2, Jing Xia3

1. 1. Institute of Information and System Science, Beifang University for Nationalities, Yinchuan 750021, China;
2. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China;
3. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China
• Received:2012-09-11 Online:2013-02-15 Published:2013-01-22

A branch-and-bound reduced method is proposed for globally solving a class of linear multiplicative programming problems and the convergence of the algorithm is proved. In this algorithm, the lower bound functions on the multiplications in the constraints and the objective functions are given by using the convex envelopes technique of the two-vector multiplications so as to determine a relaxed convex programming of the original problem. We solve the relaxed convex programming to find the global optimization value's lower bound the feasible solutions of the original problem.In order to improve convergence rate, a rectangular reduction strategy is used. Numerical experiments show that the proposed algorithm is feasible.

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