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Pure Mathematics 2016
梯度法求解黎曼流行上的多指标最优化
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Abstract:
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.
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http://dx.doi.org/10.1007/s10957-011-9984-2 |
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