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积分第二中值定理“中间点”的渐近性 被引量:26
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作者 吴至友 夏雪 《数学的实践与认识》 CSCD 北大核心 2004年第3期170-176,共7页
给出了在各种情况下积分第二中值定理“中间点”的渐近性的几个结论 ,相信在积分学中有着很重要的作用 .
关键词 积分第二中值定理 “中间点” 渐近性 数学分析
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基于上下边缘点匹配的连通域搜索算法 被引量:8
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作者 谢贵 彭嘉雄 《华中科技大学学报(自然科学版)》 EI CAS CSCD 北大核心 2002年第4期64-65,68,共3页
基于上下边缘点匹配的连通域搜索算法利用连通域的上下边缘点是一一对应的这一基本原理 ,设计出新的高效二值图像连通域搜索方法 .该算法能在行扫描图像过程中提取连通域 .给出了实验分析数据 ,并与行程标记法进行了时间复杂度的比较 ,... 基于上下边缘点匹配的连通域搜索算法利用连通域的上下边缘点是一一对应的这一基本原理 ,设计出新的高效二值图像连通域搜索方法 .该算法能在行扫描图像过程中提取连通域 .给出了实验分析数据 ,并与行程标记法进行了时间复杂度的比较 ,验证了该算法的有效性 . 展开更多
关键词 图像处理 连通关系 四连通域 八连通域 上边缘点 下边缘点 内部点 搜索算法 匹配
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关于单形内点的一类几何不等式 被引量:11
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作者 杨世国 《浙江大学学报(理学版)》 CAS CSCD 2004年第5期488-490,共3页
应用解析方法和质点组几何不等式理论 ,研究了关于单形内点的几何不等式问题 ,建立了涉及单形内点的一类几何不等式 ,作为其特例得到垂足单形的几何不等式 .
关键词 单形 内点 体积 不等式
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A Large-update Interior-point Algorithm for Convex Quadratic Semi-definite Optimization Based on a New Kernel Function 被引量:9
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作者 Ming Wang ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第11期2313-2328,共16页
In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular functi... In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular function and also the usual logarithmic function. The goal of this paper is to investigate such a kernel function and show that the algorithm has favorable complexity bound in terms of the elegant analytic properties of the kernel function. The complexity bound is shown to be O(√n(logn)2 log e/n). This bound is better than that by the classical primal-dual interior-point methods based on logarithmic barrier function and in optimization fields. Some computational results recent kernel functions introduced by some authors have been provided. 展开更多
关键词 Convex quadratic semi-definite optimization kernel function interior-point algorithm^large-update method complexity
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A new primal-dual interior-point algorithm for convex quadratic optimization 被引量:9
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作者 王国强 白延琴 +1 位作者 刘勇 张敏 《Journal of Shanghai University(English Edition)》 CAS 2008年第3期189-196,共8页
In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization (CQO) based on a kernel function is presented. The proposed function has some properties that are easy for checking. These ... In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization (CQO) based on a kernel function is presented. The proposed function has some properties that are easy for checking. These properties enable us to improve the polynomial complexity bound of a large-update interior-point method (IPM) to O(√n log nlog n/e), which is the currently best known polynomial complexity bound for the algorithm with the large-update method. Numerical tests were conducted to investigate the behavior of the algorithm with different parameters p, q and θ, where p is the growth degree parameter, q is the barrier degree of the kernel function and θ is the barrier update parameter. 展开更多
关键词 convex quadratic optimization (CQO) interior-point methods (IPMs) large-update method polynomial complexity
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Primal-dual Interior-point Algorithms for Second-order Cone Optimization Based on a New Parametric Kernel Function 被引量:9
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作者 Yan Qin BAI Guo Qiang WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第11期2027-2042,共16页
A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and qu... A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O(√Nlog N log N/ε) for large-update methods and O(√Nlog N/ε) for smallupdate methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q. 展开更多
关键词 second-order cone optimization linear optimization interior-point methods large- and small-update methods polynomial-time complexity
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N指标d维广义Wiener过程象集代数和性质 被引量:9
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作者 徐赐文 《数学杂志》 CSCD 1997年第2期199-206,共8页
令W(t):RN+→Rd是N指标d维广义Wiener过程,对任意紧集E,FRN+\{0},本文研究了代数和W(E)-W(F)的Hausdorf维数及内点存在性。
关键词 象集代数和 内点 象集 维纳过程 广义
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基于网络流和内点法的电力系统动态经济调度 被引量:5
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作者 李秀卿 罗忠游 郭芳义 《继电器》 CSCD 北大核心 2006年第10期37-40,45,共5页
该文用线性约束网络流来描述电力系统动态经济调度问题,它在计及机组出力上下界约束和输电元件传输功率上下界约束的同时,也考虑了电力网络中功率的流动应遵循的自然规律—K irchhoff定律,确保了网络流模型解与直流模型解的一致性,并用... 该文用线性约束网络流来描述电力系统动态经济调度问题,它在计及机组出力上下界约束和输电元件传输功率上下界约束的同时,也考虑了电力网络中功率的流动应遵循的自然规律—K irchhoff定律,确保了网络流模型解与直流模型解的一致性,并用内点法进行求解。内点法克服了传统方法难以精确处理不等式约束的弊端,使计算结果更精确。同时采用变量重组、矩阵既约和约束松弛技术,减少计算量,加快了计算速度。计算结果表明:该文方法是可行和有效的。 展开更多
关键词 电力系统 协调方程式 内点法 网络流 安全约束 经济调度
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Numerical simulation of a gas pipeline network using computational fluid dynamics simulators 被引量:9
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作者 SELEZNEV Vadim 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2007年第5期755-765,共11页
This article describes numerical simulation of gas pipeline network operation using high-accuracy computational fluid dynamics (CFD) simulators of the modes of gas mixture transmission through long, multi-line pipelin... This article describes numerical simulation of gas pipeline network operation using high-accuracy computational fluid dynamics (CFD) simulators of the modes of gas mixture transmission through long, multi-line pipeline systems (CFD-simulator). The approach used in CFD-simulators for modeling gas mixture transmission through long, branched, multi-section pipelines is based on tailoring the full system of fluid dynamics equations to conditions of unsteady, non-isothermal processes of the gas mixture flow. Identification, in a CFD-simulator, of safe parameters for gas transmission through compressor stations amounts to finding the interior points of admissible sets described by systems of nonlinear algebraic equalities and inequalities. Such systems of equalities and inequalities comprise a formal statement of technological, design, operational and other constraints to which operation of the network equipment is subject. To illustrate the practicability of the method of numerical simulation of a gas transmission network, we compare computation results and gas flow parameters measured on-site at the gas transmission enter-prise. 展开更多
关键词 Long branched gas pipeline network UNSTEADY Non-isothermal gas flow CFD-simulator Numerical simulation Finite Volume Method interior point Method
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A Frisch-Newton Algorithm for Sparse Quantile Regression 被引量:7
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作者 Roger Koenker Pin Ng 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2005年第2期225-236,共12页
Recent experience has shown that interior-point methods using a log barrierapproach are far superior to classical simplex methods for computing solutions to large parametricquantile regression problems. In many large ... Recent experience has shown that interior-point methods using a log barrierapproach are far superior to classical simplex methods for computing solutions to large parametricquantile regression problems. In many large empirical applications, the design matrix has a verysparse structure. A typical example is the classical fixed-effect model for panel data where theparametric dimension of the model can be quite large, but the number of non-zero elements is quitesmall. Adopting recent developments in sparse linear algebra we introduce a modified version of theFrisch-Newton algorithm for quantile regression described in Portnoy and Koenker[28]. The newalgorithm substantially reduces the storage (memory) requirements and increases computational speed.The modified algorithm also facilitates the development of nonparametric quantile regressionmethods. The pseudo design matrices employed in nonparametric quantile regression smoothing areinherently sparse in both the fidelity and roughness penalty components. Exploiting the sparsestructure of these problems opens up a whole range of new possibilities for multivariate smoothingon large data sets via ANOVA-type decomposition and partial linear models. 展开更多
关键词 Quantile regression interior-point algorithm sparse linear algebra
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A New Kernel Function Yielding the Best Known Iteration Bounds for Primal-Dual Interior-Point Algorithms 被引量:7
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作者 Yan Qin BAI Jin LiGUO Cornelis ROOS 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第12期2169-2178,共10页
Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields ... Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields an algorithm with the best known complexity bound for both large- and small-update methods. 展开更多
关键词 linear optimization interior-point method primal-dual method large-update method polynomial complexity
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一类具有二个转向点的大参数奇摄动方程 被引量:7
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作者 莫嘉琪 《系统科学与数学》 CSCD 北大核心 2007年第5期684-690,共7页
利用匹配方法研究了一类具有二个转向点的大参数奇摄动方程.得出了解在不同范围内的渐近表示式.
关键词 奇摄动 外部解 内层 转向点
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Path-following interior point algorithms for the Cartesian P_*(κ)-LCP over symmetric cones 被引量:5
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作者 LUO ZiYan XIU NaiHua 《Science China Mathematics》 SCIE 2009年第8期1769-1784,共16页
In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condi... In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms. 展开更多
关键词 Cartesian P *(κ)-property symmetric cone linear complementarity problem path-following interior point algorithm global convergence COMPLEXITY 90C33 90C51
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A class of polynomial primal-dual interior-point algorithms for semidefinite optimization 被引量:6
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作者 王国强 白延琴 《Journal of Shanghai University(English Edition)》 CAS 2006年第3期198-207,共10页
In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to... In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to its growth term increasing linearly. Some new analysis tools were developed which can be used to deal with complexity "analysis of the algorithms which use analogous strategy in [5] to design the search directions for the Newton system. The complexity bounds for the algorithms with large- and small-update methodswere obtained, namely,O(qn^(p+q/q(P+1)log n/ε and O(q^2√n)log n/ε,respectlvely. 展开更多
关键词 semidefinite optimization (SDO) primal-dual interior-point methods large- and small-update methods polynomial complexity
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有界变量约束优化的仿射投影共轭梯度路径内点方法 被引量:4
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作者 林涛 朱德通 《上海师范大学学报(自然科学版)》 2005年第3期11-16,共6页
采用共轭梯度路径结合仿射内点投影回代技术解有界变量约束的非线性优化问题.通过构造共轭梯度路径解二次模型获得搜索方向,引入线搜索技术获得的迭代步既落在严格可行域内,又能使目标函数下降.基于共轭梯度路径的性质,在合理的假设条件... 采用共轭梯度路径结合仿射内点投影回代技术解有界变量约束的非线性优化问题.通过构造共轭梯度路径解二次模型获得搜索方向,引入线搜索技术获得的迭代步既落在严格可行域内,又能使目标函数下降.基于共轭梯度路径的性质,在合理的假设条件下,证明了所提供的算法不仅具有整体收敛性,而且保持快速的超线性收敛速率.进一步,数值计算说明了算法的可行性和有效性. 展开更多
关键词 有界变量约束 共轭梯度路径 内点法 仿射投影
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Neighborhood-following algorithms for linear programming 被引量:7
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作者 Al WenbaoSchool of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China 《Science China Mathematics》 SCIE 2004年第6期812-820,共9页
In this paper, we present neighborhood-following algorithms for linear programming. When the neighborhood is a wide neighborhood, our algorithms are wide neighborhood primal-dual interior point algorithms. If the neig... In this paper, we present neighborhood-following algorithms for linear programming. When the neighborhood is a wide neighborhood, our algorithms are wide neighborhood primal-dual interior point algorithms. If the neighborhood degenerates into the central path, our algorithms also degenerate into path-following algorithms. We prove that our algorithms maintain the O9√nL) -iteration complexity still, while the classical wide neighborhood primal-dual interior point algorithms have only the O(nL-iteration complexity. We also proved that the algorithms are quadratic convergence if the optimal vertex is nondegenerate. Finally, we show some computational results of our algorithms. 展开更多
关键词 linear programming primal-dual interior point methods wide neighborhood methods quadratic convergence
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具有二阶转向点的大参数奇摄动方程 被引量:6
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作者 莫嘉琪 《厦门大学学报(自然科学版)》 CAS CSCD 北大核心 2005年第6期753-755,共3页
讨论了一类二阶常微分方程并具有高阶转向点的大参数的奇异摄动问题.首先将方程同时作自变量和因变量的Liouville-Green变换,得到问题的外部解.然后引入伸展变量变换,并利用1/4和-1/4阶Bessel函数,构造在转向点附近的内层解.最后从解在... 讨论了一类二阶常微分方程并具有高阶转向点的大参数的奇异摄动问题.首先将方程同时作自变量和因变量的Liouville-Green变换,得到问题的外部解.然后引入伸展变量变换,并利用1/4和-1/4阶Bessel函数,构造在转向点附近的内层解.最后从解在不同区域的表示式,利用匹配原理适当地选取任意常数,将外部解和内层解进行匹配得到问题解的匹配条件.从而得到在整个区域内的一致有效的渐近解的不同表示式. 展开更多
关键词 奇摄动 外部解 内层 转向点
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基于等间距平行线区域填充算法 被引量:7
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作者 邱国清 《内蒙古农业大学学报(自然科学版)》 CAS 2017年第2期89-92,共4页
多边形区域填充的递归种子填充算法存在一个点多次进入堆栈和扫描线种子填充算法重复判断大量像素点的缺陷,为此提出一种基于等间距平行线区域填充新算法,首先采用Douglas-Peuker算法对复杂多边形化简,其次采用等间距平行线绘制多边形区... 多边形区域填充的递归种子填充算法存在一个点多次进入堆栈和扫描线种子填充算法重复判断大量像素点的缺陷,为此提出一种基于等间距平行线区域填充新算法,首先采用Douglas-Peuker算法对复杂多边形化简,其次采用等间距平行线绘制多边形区域,最后计算每条平行线经过内点的个数及相应的行列值,完成区域填充。实验数据验证,该算法填充效率良好,无需对内点重复判断,特别适合于多边形嵌套的区域填充。 展开更多
关键词 Douglas-Peuker算法 等间距平行线 内点 行列值 区域填充
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可分凸二次规划的不可行内点算法 被引量:5
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作者 李健 费浦生 邱巍 《武汉大学学报(自然科学版)》 CSCD 2000年第5期531-534,共4页
给出了可分凸二次规划的不可行内点算法 ,并证明了该算法在 O(n2 L )次迭代之后 ,或者收敛到问题的一个近似最优解 ,或者说明该问题在某个较大区域内无最优解 .
关键词 可分凸二次规划 内点算法 多项式算法
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R^n空间中开集、闭集的新表述及其特点 被引量:5
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作者 魏勇 《西华师范大学学报(自然科学版)》 2009年第4期351-353,共3页
避开了《实变函数》、《泛函分析》两门课程中的"所有点全为内点的集为开集,包含所有极限点的集为闭集"这一较抽象的传统定义,给出了一个易于理解,但内容与原定义完全等价的新定义:不含边界点的集称为开集,包含所有边界点的... 避开了《实变函数》、《泛函分析》两门课程中的"所有点全为内点的集为开集,包含所有极限点的集为闭集"这一较抽象的传统定义,给出了一个易于理解,但内容与原定义完全等价的新定义:不含边界点的集称为开集,包含所有边界点的集称为闭集.并通过一些相关定理的证明展示了新定义的优越性. 展开更多
关键词 开集 闭集 内点 极限点 边界点
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