| 拉格朗日-拟牛顿法解约束非线性规划问题 |
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| 引用本文： | 桂胜华,周岩.拉格朗日-拟牛顿法解约束非线性规划问题[J].同济大学学报(自然科学版),2007,35(4):556-561. |
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| 作者姓名： | 桂胜华 周岩 |
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| 作者单位： | 1. 同济大学数学系,上海,200092;上海第二工业大学理学院,上海,201029
2. 同济大学数学系,上海,200092;青岛大学管理科学与工程学院,山东,青岛,266071 |
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| 基金项目： | 国家自然科学基金;上海市教委资助项目 |
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| 摘 要： | Partier E R和祁力群等人先后提出解光滑不等式约束函数和光滑目标函数最优化问题的QP-free方法，算法中所有的迭代点为可行点．笔者在先前发表的文章中，提出了含弱互补函数的不等式约束最优化问题的拉格朗日-牛顿法．现笔者改进了先前文章中算法，用拟牛顿公式代替了Hesse矩阵，把解不等式约束最优化问题推广到了既含不等式约束又含等式约束最优化问题，并证明了此算法具有全局收敛性．对一些算例的计算表明，此法具有很好的应用前景．
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| 关 键 词： | K-K-T点 拉格朗日-牛顿法 拟牛顿法 收敛性 |
| 文章编号： | 0253-374X（2007）04-556-06 |
| 修稿时间： | 2005-08-31 |
A Lagrange-Quasi Newton Method for Constraint Optimization |
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| GUI Shenghua,ZHOU Yan.A Lagrange-Quasi Newton Method for Constraint Optimization[J].Journal of Tongji University(Natural Science),2007,35(4):556-561. |
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| Authors: | GUI Shenghua ZHOU Yan |
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| Institution: | 1. Department of Mathematics, Tongji University,Shanghai 200092, China; 2. School of Science, Shanghai Second Polytechnic University Shanghai 201029,China; 3.Department of Management Science and Engineering,Qingdao University Qingdao 266071,China |
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| Abstract: | Panier E R and QI Liqun proposed the QP-free method for the minimization of a smooth function subject to smooth inequality constraints, which ensured the feasibility of all iterates. Based on a former proposal of a Lagrange-Newton method with slack NCP function for constraint optimization, this paper presents a new Lagrange-Quasi-Newton method with the slack NCP function for inequality constraint optimization. QuasiNewton method is used instead of Hessian matrix in the new method. The method is globally convergent. Some preliminary numerical results indicate that this new method is quite promising. |
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| Keywords: | K-K-T point Lagrange- Newton method quasi- Newton method convergence |
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