Riemannian Interior Point Methods for Constrained Optimization on Manifolds
Riemannian Interior Point Methods for Constrained Optimization on Manifolds
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DOI：
10.1007/s10957-024-02403-8
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发表时间：
2022-03
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影响因子：
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通讯作者：
Zhijian Lai;Akiko Yoshise
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文献类型：
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作者：
Zhijian Lai;Akiko Yoshise
我们将经典的原始-对偶内点方法从欧氏环境推广到黎曼环境。我们的方法，称为黎曼内点方法，是解决黎曼约束优化问题。在标准假设下，我们证明了它的局部超线性和二次收敛性。此外，我们证明了它的全局收敛性，当它与经典的线搜索相结合。我们的方法是一个推广的经典框架的原始-对偶内点方法的非线性非凸规划。数值实验表明了该方法的稳定性和有效性。
We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish its local superlinear and quadratic convergence under the standard assumptions. Moreover, we show its global convergence when it is combined with a classical line search. Our method is a generalization of the classical framework of primal-dual interior point methods for nonlinear nonconvex programming. Numerical experiments show the stability and efficiency of our method.