黎曼流形上多目标优化的无约束最速下降法
Unconstrained steepest descent method for multicriteria optimization on Riemmanian manifolds
AI总结：
提出黎曼流形上带Armijo规则的多目标最速下降法，证明序列良定义性、聚点满足Pareto最优一阶必要条件，并在拟凸性和非负曲率下证明序列收敛到Pareto临界点。
摘要：
本文提出了黎曼流形上带Armijo规则的多目标优化最速下降法。保证了该方法生成的序列的良定义性。在多目标函数的温和假设下，我们证明了每个聚点（如果存在）满足Pareto最优性的一阶必要条件。此外，假设多目标函数拟凸且黎曼流形曲率非负，我们证明了序列完全收敛到Pareto临界点。
英文摘要：
In this paper we present a steepest descent method with Armijo's rule for multicriteria optimization in the Riemannian context. The well definedness of the sequence generated by the method is guaranteed. Under mild assumptions on the multicriteria function, we prove that each accumulation point (if they exist) satisfies first-order necessary conditions for Pareto optimality. Moreover, assuming quasi-convexity of the multicriteria function and non-negative curvature of the Riemannian manifold, we prove full convergence of the sequence to a Pareto critical.
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