A Use of Conjugate Gradient Direction for the Convex Optimization Problem over the Fixed Point Set of a Nonexpansive Mapping
A Use of Conjugate Gradient Direction for the Convex Optimization Problem over the Fixed Point Set of a Nonexpansive Mapping
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DOI：
10.1137/070702497
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发表时间：
2008-12
期刊：
影响因子：
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通讯作者：
H. Iiduka;I. Yamada
中科院分区：
文献类型：
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作者：
H. Iiduka;I. Yamada
本文讨论了非扩张映射不动点集上的凸优化问题。本文的主要目的是加速混合最速下降法的问题。为此，我们提出了一种新的迭代格式，利用共轭梯度方向。在一定的假设条件下，保证了算法的收敛性。为了证明我们所提出的算法的有效性，性能和收敛性，我们提出的算法与现有算法的数值比较。
In this paper, we discuss the convex optimization problem over the fixed point set of a nonexpansive mapping. The main objective of the paper is to accelerate the hybrid steepest descent method for the problem. To this goal, we present a new iterative scheme that utilizes the conjugate gradient direction. Its convergence to the solution is guaranteed under certain assumptions. In order to demonstrate the effectiveness, performance, and convergence of our proposed algorithm, we present numerical comparisons of the algorithm with the existing algorithm.