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拉格朗日-拟牛顿法解约束非线性规划问题 被引量：17

A Lagrange-Quasi Newton Method for Constraint Optimization
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摘要 Panier 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. 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.
作者 桂胜华 周岩
机构地区 同济大学数学系
出处 《同济大学学报（自然科学版）》 EI CAS CSCD 北大核心 2007年第4期556-561,共6页 Journal of Tongji University:Natural Science
基金 国家自然科学基金资助项目(10571137) 上海市教委科研基金资助项目(05RZ12)
关键词 K—K—T点 拉格朗日-牛顿法 拟牛顿法 收敛性 K-K-T point Lagrange- Newton method quasi- Newton method convergence
分类号 O221.2 [理学—运筹学与控制论]
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参考文献14

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二级参考文献21

  • 1桂胜华,张倩,邢丽,徐玲.弱互补函数的拉格朗日-拟牛顿法[J].上海第二工业大学学报,2005,22(5):21-27. 被引量：8
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  • 9Qi H and Qi L. A New QP-free, globally V, locally superlinear convergent feasible method for the solution of inequality constrained optimization problems[J]. SIAM J. Optim., 2000,11: 113--132.
  • 10Harker P T,Pang J S.Finite-dimensional variational and nonlinear complementarity problems:a survey of theory,algorithm and applications[J].Mathematical Programming,1990,48:161.

共引文献7

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引证文献17

二级引证文献43

同济大学学报（自然科学版）
2007年 第4期

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