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
DOI: 10.12677/PM.2016.61002, PDF,    科研立项经费支持
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. 梯度法求解黎曼流行上的多指标最优化[J]. 理论数学, 2016, 6(1): 10-16. https://dx.doi.org/10.12677/PM.2016.61002

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