| BANACH空间中的最速下降法 |
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| 引用本文： | 李文林.BANACH空间中的最速下降法[J].河南师范大学学报(自然科学版),1987(2). |
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| 作者姓名： | 李文林 |
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| 作者单位： | 河南师范大学数学系 |
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| 摘 要： | 本文应用Gateaux导数和泛函分析理论给出了弱紧Banach空间中的最速下降方向和达到最优点的条件,然后用Riesz表示定理讨论了Hilbert空间的三种下降方向,指出了它们的共同特征和在线性赋范空间中应用的可能性。
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| 关 键 词： | 最速下降 最优化 弱紧 Gateaux 导数 |
THE METHOD OF STEEPEST DESCENT IN BANACH SPACE |
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| Li Wenlin.THE METHOD OF STEEPEST DESCENT IN BANACH SPACE[J].Journal of Henan Normal University(Natural Science),1987(2). |
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| Authors: | Li Wenlin |
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| Abstract: | In this article we discuss the method of steepest descemt for the functions in Banach space. By the means of Gateaux deriative and theory of functional analysis we find a direction of steepest descent in the weak compact Banach space. Then using Riesz＇s representive theorm, we give a descent direction in Hilbert space. At last we point out that their ortho-gonal character is also used in the linear normal space. |
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| Keywords: | steepest descent weak compact minimization Gateaux deriative |
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