Subgradient Projection Algorithms for Convex Feasibility on Riemannian Manifolds with Lower Bounded Curvatures
Subgradient Projection Algorithms for Convex Feasibility on Riemannian Manifolds with Lower Bounded Curvatures
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DOI：
10.1007/s10957-014-0568-9
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发表时间：
2014-04
影响因子：
1.9
通讯作者：
Xiangmei Wang;Chong Li;J. Yao
中科院分区：
文献类型：
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作者：
Xiangmei Wang;Chong Li;J. Yao
在流形截面曲率自下有界的假设下，我们建立了Bento和Melo在黎曼流形上提出的解凸可行性问题的循环次梯度投影算法的收敛结果(J OpTim理论应用152,773-785,2012)。另外，如果我们假设满足一个斯莱特类型的条件，那么我们进一步证明了，在不改变步长的情况下，该算法在有限次迭代中终止。显然，我们的结果推广了Bento和Melo的相应结果，特别是我们部分地解决了Bento和Melo在论文中提出的公开问题。
Under the assumption that the sectional curvature of the manifold is bounded from below, we establish convergence result about the cyclic subgradient projection algorithm for convex feasibility problem presented in a paper by Bento and Melo on Riemannian manifolds (J Optim Theory Appl 152, 773–785, 2012). If, additionally, we assume that a Slater type condition is satisfied, then we further show that, without changing the step size, this algorithm terminates in a finite number of iterations. Clearly, our results extend the corresponding ones due to Bento and Melo and, in particular, we solve partially the open problem proposed in the paper by Bento and Melo.