梯度法求解黎曼流行上的多指标最优化
A Gradient Method to Solve Multicriteria Optimization on Riemannian Manifolds

作者: 唐凤梅 :上海大学理学院数学系,上海;

关键词: 多指标最优化伪凸拟凸Pareto最优黎曼流形Multicriteria Optimization Pseudo-Convexity Quasiconvexity Pareto Optimality Riemannian Manifolds

摘要:

在这篇文章中,我们提出了黎曼流形上的一种新的梯度法,来解决多指标最优化问题。当目标函数是拟凸时,由梯度法产生的迭代序列收敛到临界的Pareto点,若目标函数是伪凸的,则由新的梯度算法产生的迭代序列收敛到最优的Pareto点。

In this paper, we present a new gradient method in the Riemannian context to solve multicriteria optimization. If the objective function is quasiconvex, the sequence generated by this method converges to a critical Pareto point. If the objective function is pseudo-convex, then the sequence will converge to optimal Pareto point.

文章引用: 唐凤梅 (2016) 梯度法求解黎曼流行上的多指标最优化。 理论数学, 6, 10-16. doi: 10.12677/PM.2016.61002

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