非凸优化中一种带非单调线搜索的惯性邻近算法

An Inertial Proximal Algorithm with Non-Monotone Line Search for Non-Convex Optimization

本文考虑一类目标函数由可微(可能非凸)函数和凸(可能非光滑)函数组成的极小化问题。惯性邻近(iPiano)算法是解决这类问题的一种有效而重要的方法。通过引入非单调线搜索,提出了非单调线搜索的iPiano (iPiano-nml)算法。通过证明说明了由iPiano-nml生成的序列的任何聚点都是一个稳定点。最后,对图像处理问题进行了数值实验来说明新算法的理论结果。

We consider a class of minimization problems whose objective function is composed of a differentiable (possibly nonconvex) function and a convex (possibly nonsoomth) function. The inertial proximal algorithm is a common and important method for this kind of problems. By incorporating the non-monotone line search, iPiano algorithm with non-monotone line search is proposed. We show that any cluster point of sequence which is generated by iPiano-nml is a stationary point. Finally, we perform numerical experiments on the image processing problems to illustrate our theoretical results.