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Iteration-Complexity and Asymptotic Analysis of Steepest Descent Method for Multiobjective Optimization on Riemannian Manifolds

Author

Listed:
  • Orizon P. Ferreira

    (Universidade Federal de Goiás)

  • Mauricio S. Louzeiro

    (TU Chemnitz)

  • Leandro F. Prudente

    (Universidade Federal de Goiás)

Abstract

The steepest descent method for multiobjective optimization on Riemannian manifolds with lower bounded sectional curvature is analyzed. The aim of this study is twofold. First, an asymptotic analysis of the method is presented with three different finite procedures for determining the stepsize: Lipschitz, adaptive, and Armijo-type stepsizes. Second, by assuming the Lipschitz continuity of a Jacobian, iteration-complexity bounds for the method with these three stepsize strategies are presented. In addition, some examples that satisfy the hypotheses of the main theoretical results are provided. Finally, the aforementioned examples are presented through numerical experiments.

Suggested Citation

  • Orizon P. Ferreira & Mauricio S. Louzeiro & Leandro F. Prudente, 2020. "Iteration-Complexity and Asymptotic Analysis of Steepest Descent Method for Multiobjective Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 507-533, February.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:2:d:10.1007_s10957-019-01615-7
    DOI: 10.1007/s10957-019-01615-7
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    References listed on IDEAS

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    1. N. Eslami & B. Najafi & S. M. Vaezpour, 2023. "A Trust Region Method for Solving Multicriteria Optimization Problems on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 212-239, January.
    2. X. M. Wang & J. H. Wang & C. Li, 2023. "Convergence of Inexact Steepest Descent Algorithm for Multiobjective Optimizations on Riemannian Manifolds Without Curvature Constraints," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 187-214, July.

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