标题:
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
关键字:
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
期刊名称:
《Pure Mathematics》, Vol.6 No.1, 2016-01-20
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.