Abstract. 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 ε-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.
By utilizing ǫ-subgradient-oriented descent directions and the generalized Wolfe line-search on Riemannian manifold, Hosseini, Huang and Yousefpour REF presented a nonsmooth Riemannian line search algorithm and established the convergence to a stationary point.
Line Search Algorithms for Locally Lipschitz Functions on Riemannian Manifolds
SIAM Journal on Optimization
SIAM Journal on Optimization
Mathematics Computer Science