| 约束非线性l1问题的调节熵函数法 |
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| 引用本文： | 王若鹏,邢志栋.约束非线性l1问题的调节熵函数法[J].系统工程与电子技术,2005,27(2). |
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| 作者姓名： | 王若鹏 邢志栋 |
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| 作者单位： | 1. 北京石油化工学院数理部,北京,102617
2. 西北大学数学系,陕西,西安,710069 |
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| 基金项目： | 陕西省教委专项基金资助课题(01Jk057) |
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| 摘 要： | 针对约束非线性l1问题不可微的特点,提出了一种光滑函数的近似逼近方法。该方法利用调节熵函数和罚函数技术将约束非线性l1问题转化为无约束可微优化问题,因而可利用光滑优化的经典算法求出原问题的近似最优解。给出了基于光滑优化问题的BFGS迭代,并介绍了约束非线性l1问题的调节熵函数的有关性质、算法的迭代步骤及其收敛性分析。最后通过数值实例表明了该算法的有效性。
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| 关 键 词： | 非线性l1问题 调节熵函数 全局收敛性 算法 |
Adjustable entropy function method for constraint nonlinear l1 problem |
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| WANG Ruo-peng,XING Zhi-dong.Adjustable entropy function method for constraint nonlinear l1 problem[J].System Engineering and Electronics,2005,27(2). |
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| Authors: | WANG Ruo-peng XING Zhi-dong |
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| Affiliation: | WANG Ruo-peng~1,XING Zhi-dong~2 |
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| Abstract: | An approximation algorithm of smooth function is proposed to study the non-differentiable constraint nonlinear l\-1 problem. Based on adjustable entropy function and penalty function, the constraint nonlinear l\-1 problem is converted to an unconstraint differentiable problem. Then the optimal solution is obtained by BFGS iteration. Some properties of new approximate function are presnted and then the global convergence is studied according to this algorithm. The numerical result shows that the algorithm is effective. |
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| Keywords: | nonlinear l\-1 problem adjustable entropy function global convergecence algorithm |
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