Line Search Algorithms for Locally Lipschitz Functions on Riemannian Manifolds
该文针对黎曼流形上的局部Lipschitz函数，推广了非光滑Wolfe条件，提出基于ε-次梯度的线搜索算法并证明收敛性，同时将BFGS算法扩展到非光滑情形，数值实验验证了算法有效性。
This paper presents line search algorithms for finding extrema of locally Lipschitz functions defined on Riemannian manifolds. To this end we generalize the so-called Wolfe conditions for nonsmooth functions on Riemannian manifolds. Using <em>ε</em>-subgradient-oriented descent directions and the Wolfe conditions, we propose a nonsmooth Riemannian line search algorithm and establish the convergence of our algorithm to a stationary point. Moreover, we extend the classical BFGS algorithm to nonsmooth functions on Riemannian manifolds. Numerical experiments illustrate the effectiveness and efficiency of the proposed algorithm.