不可微方程的拟牛顿法
首发时间:2013-09-13
摘要:为了提高求解不可微方程的效率,同时作为对传统拟牛顿法的改进,本文给出了求解不可微方程的拟牛顿法。本文首先给出了该算法的详细描述,其次若进一步地假设该不可微方程满足局部Lipschitz连续且半光滑等条件的话,证明了该算法的全局收敛性。另外,文中利用了非精确搜索的技巧保证了拟牛顿算法的平稳收敛。本文得出的结论为:当不可微方程满足文中所提出的两个假设条件时,该迭代格式所产生的向量序列收敛于不可微方程的唯一解。
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The quasi- Newton method for non-differentiable equation
Abstract:In order to improve the efficiency of solving non-differentiable equation, as both the traditional quasi-Newton method improvement, in the paper the quasi-Newton method for differentiable equation is presented.Firstly a detailed description of the algorithm is given, secondly if the further assumption that the non-differentiable equation satisfied locally Lipschitz continuous and semi-glossy and other conditions, the global convergence of the algorithm is proved.In addition, a non-precision search technique is used to ensure a smooth quasi-Newton algorithm converges.So we can conclude that if two assumptions proposed in this paper are satisfied, the iterative sequence generated by the vector equation converges to the unique solution of non-differentiable equation.
Keywords: non-differentiable equation the quasi- Newton method global convergence
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