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Riemannian Interior Point Methods for Constrained Optimization on Manifolds

Author

Listed:
  • Zhijian Lai

    (University of Tsukuba)

  • Akiko Yoshise

    (University of Tsukuba)

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.

Suggested Citation

  • Zhijian Lai & Akiko Yoshise, 2024. "Riemannian Interior Point Methods for Constrained Optimization on Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 201(1), pages 433-469, April.
    • Handle: RePEc:spr:joptap:v:201:y:2024:i:1:d:10.1007_s10957-024-02403-8
    DOI: 10.1007/s10957-024-02403-8
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