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 a classical line search. This method is a generalization of the classical framework of primal-dual interior point methods for nonlinear programming proposed by El-Bakry et al. in 1996. Numerical experiments show the stability and efficiency of our method.

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to appear in Journal of Optimization Theory and Applications

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