Superlinear and Quadratic Convergence of Riemannian Interior Point Methods
Superlinear and Quadratic Convergence of Riemannian Interior Point Methods
复制标题
DOI：
--
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Zhijian Lai;Akiko Yoshise
中科院分区：
文献类型：
--
作者：
Zhijian Lai;Akiko Yoshise
我们将经典的原始 - 对偶内点算法从欧几里得情形推广到黎曼情形。我们的方法，称为黎曼内点（RIP）方法，用于解决黎曼约束优化问题。在黎曼情形的标准假设下，我们证明了RIP的牛顿版本具有局部超线性、二次收敛性，准牛顿版本具有局部线性、超线性收敛性。这些是1996年El - Bakry等人和Yamashita等人提出的非线性规划的原始 - 对偶内点算法的经典局部收敛理论的推广。
We extend the classical primal-dual interior point algorithms from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point (RIP) method, is for solving Riemannian constrained optimization problems. Under the standard assumptions in the Riemannian setting, we establish locally superlinear, quadratic convergence for the Newton version of RIP and locally linear, superlinear convergence for the quasi-Newton version. These are generalizations of the classical local convergence theory of primal-dual interior point algorithms for nonlinear programming proposed by El-Bakry et al. and Yamashita et al. in 1996.