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With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.
本文一方面基于现有的各种光滑Newton法的思想和半光滑理论,利用著名的F-B互补函数的光滑形式,首先将互补问题的求解转化为求解一系列光滑的非线性方程组,然后给出了一种修正的光滑Newton法,该方法不仅放宽对函数F的要求,在Newton方程不可解时引入初始效益函数的最速下降方向,而且光滑因子的选择也比较简单可行,同时在适当的条件下,证明了其算法具有全局收敛性;另一方面,借助另一种F-B光滑函数,将多面体锥上的广义互补问题转化为一种光滑形式,讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系,并将这种修正的光滑Newton法用于求解广义非线性互补问题中,在适当的条件下,该算法同样具有全局收敛性。
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The algorithm has following properties: Although the merit function has the form of least squares of a system of overdetermined equations, in the Newton equation of our algorithm, only the coefficient matrix of the system of overdetermined equations is used instead of its product as in Guass-Newton method for solving the least squares problems. That is, our Newton method is more like that for the system of nonlinear equations rather than that for LSPs. The global convergence is obtained for VLCP with vertical block P_0 + R_0 matrix; The local quadratic convergence rate is proved under the condition that the solution is BD-regular; Although there is only a Newton equation in our algorithm, the finite convergence property can be shown if matrix is vertical block P— matrix (without the hypotheses of strict complementarity).
该算法具有下列特点:所构造的价值函数虽然具有超定方程组的最小二乘问题的形式,但在基此建立的Newton算法中,其Newton方程的形式更象非线性方程组的Newton法中的Newton方程,仅利用了超定方程组的系数矩阵本身的信息,避免了一般最小二乘问题的Guass-Newton法中必须计算系数矩阵的乘积的工作量;对竖块P_0+R_0矩阵的垂直线性互补问题,算法具有全局收敛性;在解是BD-正则条件下,证明了算法的局部二次收敛性;虽然算法只含一个Newton方程,但对竖块P-矩阵垂直线性互补问题,算法具有有限步收敛性。
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It also makes analysis on the connection of Newton's prism experiments, and describes how Newton proved these propositions by taking advantage of these experiments in the article. As well the author makes analysis and generalization on the make of Newton's reflecting telescope and Newton's
首先,在对《光学》认真研读的基础上,首次对其光的颜色理论部分的大量棱镜实验之间的关系进行了分析,从而说明牛顿是如何利用这些实验证明这些命题的;其次,笔者在前人研究的基础上,对反射望远镜的制造和牛顿环理论进行分析和总结,力求描述得清楚全面;最后,鉴于国内外对牛顿光本性认识的研究存在分歧的情况,笔者对惠更斯和牛顿的相关著作进行了详细考察,对他们的光本性观点进行了系统的研究和比较,从而指出那种只因牛顿
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Newton:牛顿
普通的传统媒体的...互联网周刊:迎接口袋互联网 来源:互联网周刊 "牛顿"(Newton)到iPod touch,苹果用14年的时间,终于将Mac OX装进了普通人的口袋. 很多人都说iPod touch其实就是去掉了通信功能的iPhone,但对苹果这样的完美主义者而言,
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Newton:纽顿
这项名为城市变迁:由郊区走向城市(TownShift: Suburb Into City)的公开设计比赛,希望民众提供该市包括克洛弗代尔(Cloverdale)、弗利特伍德(Fleetwood)、吉尔福德(Guildford)、纽顿(Newton)、及西米娅姆(Semiahmoo)等5个城镇中心的
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Newton:牛顿镇
查尔斯河流域协会(The Charles River Watershed Association)就是一个代表,该协会是马萨诸塞州牛顿镇(Newton)的一个非营利性的组织. 查尔斯河流域协会联合马萨诸塞州Holliston镇进行了一个环境分区项目. 这个项目寻求从根本上推翻传统的规划方式,
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Newton:科学世界
概况: >(Newton)是由中国科学院主管的一本综合性科普月刊,旨在向广大公众传播科学技术知识,倡导科学方法,激励科学思维,促进科学生活,竭力提高我国国民的科学素养.
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"newton":magnification
"magnetizing current","磁化电流","neutron number","中子数" | "magnification","放大,放大率","newton","牛顿" | "magnified","放大的"
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