论文标题
部分可观测时空混沌系统的无模型预测
Riemannian Interior Point Methods for Constrained Optimization on Manifolds
论文作者
论文摘要
我们将经典的原始偶二个内点方法从欧几里得的设置扩展到Riemannian。我们的方法称为Riemannian Interior Point方法，用于解决Riemannian约束优化问题。我们在标准假设下建立了其局部超线性和二次收敛。此外，当它与经典的线搜索结合使用时，我们显示了它的全局收敛性。我们的方法是对非线性非convex编程的原始双重内点方法的经典框架的概括。数值实验显示了我们方法的稳定性和效率。
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.
