| 基于变分不等式KKT条件的等价关系的Levenberg-Marquardt算法 |
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| 引用本文： | 陈建芮,乌力吉,王晓民.基于变分不等式KKT条件的等价关系的Levenberg-Marquardt算法[J].黑龙江大学自然科学学报,2012,29(1):72-79. |
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| 作者姓名： | 陈建芮 乌力吉 王晓民 |
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| 作者单位： | 内蒙古工业大学理学院,呼和浩特,010062 |
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| 基金项目： | 智能感知与图像理解教育部重点实验室开放基金资助项目(IPIU012011003);内蒙古工业大学科学研究项目(X200936),内蒙古工业大学重点项目(ZD200417) |
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| 摘 要： | 建立变分不等式问题KKT条件与光滑带约束方程组的等价关系,进而转化为约束优化问题。利用Levenberg-Marquardt方法给出求解变分不等式问题的算法,在不要求梯度矩阵非奇异的条件下得到了算法的全局收敛性。该算法在一定条件下是局部超线性或二次收敛的。
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| 关 键 词： | 变分不等式问题 KKT条件 全局收敛 局部超线性或二次收敛 Levenberg-Mar-quardt算法 |
Levenberg-Marquardt algorithm based on the equivalent relation of variational inequality problem KKT conditions |
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| CHEN Jian-rui
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WU Li-ji
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WANG Xiao-min.Levenberg-Marquardt algorithm based on the equivalent relation of variational inequality problem KKT conditions[J].Journal of Natural Science of Heilongjiang University,2012,29(1):72-79. |
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| Authors: | CHEN Jian-rui WU Li-ji WANG Xiao-min |
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| Institution: | (College of Science,Inner Mongolia University of Technology,Hohhot 010062,China) |
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| Abstract: | Variational inequality is a very important field in applied mathematics and it is a key problem to obtain its solution efficiently and rapidly.The equivalent relation of variational inequality problem KKT conditions and smooth equations with constraint is first obtained,and then it is transformed to a constrained optimal problem,which can be solved by using the corresponding Levenberg-Marquardt algorithm.Under the condition without gradient matrix nonsingular,it is shown that the algorithm is global convergent.The algorithm is local super-linear convergent or quadratically convergent under the appropriate condition. |
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| Keywords: | variational equality KKT conditions global convergent local superlinear convergent or quadratically convergent Levenberg-Marquardt algorithm |
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