一种改进的动态步长的次梯度算法

A Modified Subgardient Algorithm with Dynamic Stepsizes

次梯度法是解决大规模凸优化问题的经典和有效的方法之一,步长的选取对次梯度法的收敛性起着至关重要的作用.Goffino等(1999)提出了动态步长次梯度算法,通过改进其中的一个参数,提出了改进的动态步长次梯度算法,并证明了改进算法的收敛性.最后,通过数值实验可以看出改进的算法比原来的算法更有效.

The subgradient algorithm is one of the classical and important algorithms to solve the large-scale convex optimization problems, and it is well known that the convergence of the algorithm depends heavily on the choice of the step sizes. A modified version of the dynamic step sizes proposed by Goffino(1999) was proposed and the convergence of the algorithm was established. Some numerical experiments illustrate that the new algorithm is more effective than the prior one.