Convergence of Inexact Steepest Descent Algorithm for Multiobjective Optimizations on Riemannian Manifolds Without Curvature Constraints

X. M. Wang (), J. H. Wang () and C. Li ()
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X. M. Wang: Guizhou University
J. H. Wang: Hangzhou Normal University
C. Li: Zhejiang University

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 1, No 7, 187-214

Abstract: Abstract We study the issue of convergence for inexact steepest descent algorithm (employing general step sizes) for multiobjective optimizations on general Riemannian manifolds (without curvature constraints). Under the assumption of the local convexity/quasi-convexity, local/global convergence results are established. Furthermore, without the assumption of the local convexity/quasi-convexity, but under an error bound-like condition, local/global convergence results and convergence rate estimates are presented, which are new even in the linear space setting. Our results improve/extend the corresponding ones in (Wang et al. in SIAM J Optim 31(1):172–199, 2021) for scalar optimization problems on Riemannian manifolds to multiobjective ones. Finally, for the special case when the inexact steepest descent algorithm employing Armijo rule, our results improve/extend the corresponding ones in (Ferreira et al. in J Optim Theory Appl 184:507–533, 2020) by relaxing curvature constraints.

Keywords: Riemannian manifold; Sectional curvature; Multiobjective optimization; Inexact descent algorithm; Full convergence; Convergence rate; 90C29; 65K05 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-023-02235-y

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