| 非线性优化的直接搜索算法及收敛性证明 |
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| 引用本文： | 蔡志杰,陈德强.非线性优化的直接搜索算法及收敛性证明[J].复旦学报(自然科学版),2006,45(3):396-403,411. |
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| 作者姓名： | 蔡志杰 陈德强 |
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| 作者单位： | 复旦大学,数学科学学院,上海,200433 |
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| 摘 要： | 研究非线性函数的优化问题.在很多实际问题中,会遇到求连续函数的极值问题.如果目标函数不存在导数,或者导数很难求得,一些高精度的极值计算方法就不能使用.针对这一问题给出相应的直接搜索算法,证明了算法的收敛性,并给出一些算例.最后将这一算法运用于分形粗糙面的反演问题中,得到了很好的反演效果.
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| 关 键 词： | 非线性优化 搜索算法 收敛性 分形粗糙面 反问题 |
| 文章编号： | 0427-7104（2006）03-396-08 |
| 收稿时间： | 2005-02-28 |
| 修稿时间： | 2005-02-28 |
A Direct Searching Method for Nonlinear Optimizing Problems and Its Convergence Proof |
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| CAI Zhi-jie,CHEN De-qiang.A Direct Searching Method for Nonlinear Optimizing Problems and Its Convergence Proof[J].Journal of Fudan University(Natural Science),2006,45(3):396-403,411. |
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| Authors: | CAI Zhi-jie CHEN De-qiang |
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| Institution: | School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
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| Abstract: | The optimizing problems of nonlinear functions are discussed.In a lot of practical problems,one often encounters the extreme problem of continuous functions.If the derivative of the objective function does not exist or is difficult to be calculated,some high precision optimal methods cannot be used.A direct searching method without computing the derivative functions is given.The convergence for this method is proved and applied to solve inverse problem of fractal rough surface. |
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| Keywords: | nonlinear optimization searching method convergence fractal rough surface inverse problem |
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