论文标题
Levenberg-Marquardt算法的收敛性和复杂性分析针对反问题
Convergence and Complexity Analysis of a Levenberg-Marquardt Algorithm for Inverse Problems
论文作者
论文摘要
Levenberg-Marquardt算法是找到非线性最小二乘问题解决方案的最流行算法之一。在基本过程的不同修改变化中，该算法在适当的假设下均具有全球收敛性，竞争性最差的迭代复杂性率以及零和非零小残留问题的局部收敛速率。我们介绍了一种新颖的Levenberg-Marquardt方法，该方法与单个无缝算法同时匹配了所有这些收敛属性的最新技术状态。数值实验证实了我们提出的算法的理论行为。
The Levenberg-Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a competitive worst case iteration complexity rate, and a guaranteed rate of local convergence for both zero and nonzero small residual problems, under suitable assumptions. We introduce a novel Levenberg-Marquardt method that matches, simultaneously, the state of the art in all of these convergence properties with a single seamless algorithm. Numerical experiments confirm the theoretical behavior of our proposed algorithm.
