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

Orizon P. Ferreira (), Mauricio S. Louzeiro () and Leandro F. Prudente ()
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Orizon P. Ferreira: Universidade Federal de Goiás
Mauricio S. Louzeiro: TU Chemnitz
Leandro F. Prudente: Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 2, No 10, 507-533

Abstract: 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.

Keywords: Steepest descent method; Multiobjective optimization problem; Riemannian manifold; Lower bounded curvature; Iteration-complexity bound; 90C33; 49K05; 47J25 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-019-01615-7

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