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On the Relationship Between the Kurdyka–Łojasiewicz Property and Error Bounds on Hadamard Manifolds

Author

Listed:
  • João Xavier Cruz Neto

    (Federal University of Piauí)

  • Ítalo Dowell Lira Melo

    (Federal University of Piauí)

  • Paulo Alexandre Sousa

    (Federal University of Piauí)

  • João Carlos Oliveira Souza

    (Federal University of Piauí)

Abstract

This paper studies the interplay between the concepts of error bounds and the Kurdyka–Łojasiewicz (KL) inequality on Hadamard manifolds. To this end, we extend some properties and existence results of a solution for differential inclusions on Hadamard manifolds. As a second contribution, we show how the KL inequality can be used to obtain the convergence of the gradient method for solving convex feasibility problems on Hadamard manifolds. The convergence results of the alternating projection method are also established for cyclic and random projections on Hadamard manifolds and, more generally, CAT(0) spaces.

Suggested Citation

  • João Xavier Cruz Neto & Ítalo Dowell Lira Melo & Paulo Alexandre Sousa & João Carlos Oliveira Souza, 2024. "On the Relationship Between the Kurdyka–Łojasiewicz Property and Error Bounds on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 200(3), pages 1255-1285, March.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:3:d:10.1007_s10957-024-02386-6
    DOI: 10.1007/s10957-024-02386-6
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