Riemannian Interior Point Methods for Constrained Optimization on Manifolds

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 (RIPM), is for solving RiemannianĀ  constrained optimization problems. We establish its local superlinear and quadratic convergenceĀ  under the standard assumptions. Moreover, we show its global convergence when it is combined with … Read more