Linear Convergence of Subgradient Algorithm for Convex Feasibility on Riemannian Manifolds
研究了黎曼流形上求解凸可行性问题的次梯度算法的收敛性，在Slater条件下证明了线性收敛，并给出了有限步收敛的步长规则，同时得到了无Slater条件时的收敛结果。
We study the convergence issue of the subgradient algorithm for solving the convex feasibility problems in Riemannian manifolds, which was first proposed and analyzed by Bento and Melo [J. Optim. Theory Appl., 152 (2012), pp. 773--785]. The linear convergence property about the subgradient algorithm for solving the convex feasibility problems with the Slater condition in Riemannian manifolds are established, and some step sizes rules are suggested for finite convergence purposes, which are motivated by the work due to De Pierro Iusem [Appl. Math. Optim., 17 (1988), pp. 225--235]. As a by-product, the convergence result of this algorithm is obtained for the convex feasibility problem without the Slater condition assumption. These results extend and/or improve the corresponding known ones in both the Euclidean space and Riemannian manifolds.