论文标题
用于优化非平滑非凸组成的歧管抽样
Manifold Sampling for Optimizing Nonsmooth Nonconvex Compositions
论文作者
论文摘要
我们提出了一种歧管算法，用于最大程度地减少非平滑构图$ f = h \ circ f $，我们假设$ h $是非平滑的，并且可以廉价地以封闭形式计算出来，$ f $很顺畅，但其jacobian可能不可用。我们还假设构图$ h \ circ f $定义了连续选择。歧管采样算法可以分类为基于模型的无衍生化方法，因为$ f $的模型与有关$ h $的采样信息结合在一起，以产生本地模型，以在信任区域框架内使用。我们证明，由歧管采样算法生成的迭代序列的群集点是Clarke Standary。我们考虑了由歧管采样算法产生的三个特定子问题的障碍，以及可以容忍对这些子问题的不精确溶液的程度。数值结果表明，作为无衍生算法的歧管采样具有竞争力，具有最新的算法，用于非平滑优化，利用有关$ f $的一阶信息。
We propose a manifold sampling algorithm for minimizing a nonsmooth composition $f= h\circ F$, where we assume $h$ is nonsmooth and may be inexpensively computed in closed form and $F$ is smooth but its Jacobian may not be available. We additionally assume that the composition $h\circ F$ defines a continuous selection. Manifold sampling algorithms can be classified as model-based derivative-free methods, in that models of $F$ are combined with particularly sampled information about $h$ to yield local models for use within a trust-region framework. We demonstrate that cluster points of the sequence of iterates generated by the manifold sampling algorithm are Clarke stationary. We consider the tractability of three particular subproblems generated by the manifold sampling algorithm and the extent to which inexact solutions to these subproblems may be tolerated. Numerical results demonstrate that manifold sampling as a derivative-free algorithm is competitive with state-of-the-art algorithms for nonsmooth optimization that utilize first-order information about $f$.
