报告人：申培萍

报告时间：12月15日周日16：00

报告地点：数学院南研

内容摘要：

The fractional optimization is quite attractive and challenging from the viewpoint of the optimization theory and methods. And it arises in various economic applications as well as real-life problems, regardless of one ratio or the sum of several ratios are required to be optimized. While there are a lot of efficient algorithms for the single ratio case, less work has been devoted to solving the sum of ratios problems. In this talk, we consider two classes of fractional programming problems, the first case is the sum of linear ratios problem, and the second one is the sum of the generalized polynomial ratios problem with generalized polynomial constraints. For the first case, an approximation algorithm is presented and the computational cost of such an algorithm is given, besides, a new accelerating technique is introduced to improve the computational efficiency of the algorithm. For the second case, a practicable contraction approach is proposed and the novel equivalence transformation as well as contraction strategies are exhibited, then the solution of the original problem can be obtained through solving a series of standard geometric programming problems. Finally, the feasibility and effectiveness of these proposed algorithms are demonstrated by some numerical experiments.

报告人简介:

申培萍,博士,教授，博士生导师，中国运筹学会理事，中国运筹学会数学规划分会常务理事，河南省运筹学会副理事长，河南省数字图形图像学会常务理事，河南省教育厅学术技术带头人。主要从事最优化理论、算法及其在工程领域中的应用研究，特别是对广义分数规划、广义几何规划等问题提出一系列全局优化求解算法。先后主持国家自然科学基金面上项目3项、河南省杰出青年基金、河南省高校科技创新人才支持计划、河南省自然科学基金等多项研究课题。发表研究论文50余篇，其中SCI论文40余篇，独著学术著作《全局优化方法》2006年在科学出版社出版，获河南省科学技术进步奖及河南省教学成果奖等。