An Efficient Global Optimization Algorithm for Nonlinear Sum-of-Ratios Problem ∗ †
An Efficient Global Optimization Algorithm for Nonlinear Sum-of-Ratios Problem ∗ †
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发表时间：
2012
影响因子：
4.1
通讯作者：
Yunchol Jong
中科院分区：
文献类型：
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作者：
Yunchol Jong
针对图像处理、工程和管理中出现的非线性比例求和问题，提出了一种求全局最优解的实用方法。不同于传统方法由于问题的非凸性而可能陷入局部极小，我们的方法提供了全局最优性的理论保证。该算法基于求解一系列凸规划问题，具有全局线性和局部超线性/二次收敛速度。通过对合成数据的数值实验，证明了该算法的实际有效性。2010年数学科目分类：90C26、90C32、65K05
This paper presents a practical method for finding the globally optimal solution to nonlinear sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to the non-convex nature of this problem, our approach provides a theoretical guarantee of global optimality. Our algorithm is based on solving a sequence of convex programming problems and has global linear and local superlinear/quadratic rate of convergence. The practical efficiency of the algorithm is demonstrated by numerical experiments for synthetic data. 2010 Mathematics subject Classification: 90C26, 90C32, 65K05