Riemannian Interior Point Methods for Constrained Optimization on Manifolds

Zhijian Lai () and Akiko Yoshise ()
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Zhijian Lai: University of Tsukuba
Akiko Yoshise: University of Tsukuba

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 1, No 17, 433-469

Abstract: Abstract 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.

Keywords: Riemannian manifolds; Riemannian optimization; Nonlinear optimization; Interior point method; 65K05; 90C48 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02403-8

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