%0 Journal Article
%T 梯度法求解黎曼流行上的多指标最优化<br>A Gradient Method to Solve Multicriteria Optimization on Riemannian Manifolds
%A 唐凤梅
%J Pure Mathematics
%P 10-16
%@ 2160-7605
%D 2016
%I Hans Publishing
%R 10.12677/PM.2016.61002
%X <p>
	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。
</p>
<p>
	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.
</p>
%K 多指标最优化，伪凸，拟凸，Pareto最优，黎曼流形
%K Multicriteria Optimization
%K Pseudo-Convexity
%K Quasiconvexity
%K Pareto Optimality
%K Riemannian Manifolds
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=16791