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.
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