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1.
考虑求解目标函数为光滑损失函数与非光滑正则函数之和的凸优化问题的一种基于线搜索的邻近梯度算法及其收敛性分析,证明了在梯度局部Lipschitz连续条件下该算法是$R$-线性收敛的,并在非光滑部分为稀疏块LASSO正则函数情况下给出了误差界条件成立的证明,得到了线性收敛率。最后,数值实验结果验证了方法的有效性。  相似文献   

2.
提出求解含平衡约束数学规划问题(简记为MPEC问题)的熵函数法,在将原问题等价改写为单层非光滑优化问题的基础上,通过熵函数逼近,给出求解MPEC问题的序列光滑优化方法,证明了熵函数逼近问题解的存在性和算法的全局收敛性,数值算例表明了算法的有效性。  相似文献   

3.
本文提出了数据挖掘中求解聚类中心问题的一种新方法.这类问题属于非凸非光滑全局最优化问题.我们首先利用光滑化方法将非光滑聚类函数用光滑函数逼近,然后对光滑化问题利用填充函数搜索其全局最优点.对不同数据库的数值试验表明,本文提出的算法是可行和有效的.  相似文献   

4.
对一类特殊极大值函数非光滑方程问题的方法进行了研究,利用极大值函数和绝对值函数的光滑函数对提出的非光滑方程问题进行转化,提出了一种光滑保守DPRP共轭梯度法.在一般的条件下,给出了光滑保守DPRP共轭梯度法的全局收敛性,最后给出相关的数值实验表明方法的有效性.  相似文献   

5.
本文定义了分片线性NCP函数,并对非线性约束优化问题,提出了带有这分片NCP函数的QP-free非可行域算法.利用优化问题的一阶KKT条件,乘子和NCP函数,得到对应的非光滑方程组.本文给出解这非光滑方程组算法,它包含原始-对偶变量,在局部意义下,可看成关扰动牛顿-拟牛顿迭代算法.在线性搜索时,这算法采用滤子方法.本文给出的算法是可实现的并具有全局收敛性,在适当假设下算法具有超线性收敛性.  相似文献   

6.
本文讨论了一类非光滑凸规划问题,给出了Lagrange乘子的存在性与值函数的次可微性的关系和乘子存在的充分条件。  相似文献   

7.
龚六堂 《数学杂志》1998,18(3):285-289
本文讨论了一类非光滑凸规划问题,给出了Lagrange乘子的存在性与值函数的次可微性的关系和乘子存在的充分条件。  相似文献   

8.
本文对构成函数为Lipschitz函数的二层规划问题,利用非光滑分析工具,讨论了下层极值函数和上层复合目标函数的Lipschitz连续性,给出了这些函数的广义微分和广义方向导数的估计式。本文得到的结果为进一步研究非可微二层Lipschitz规划的最优性条件和有效算法等理论和方法问题奠定了基础。  相似文献   

9.
非线性互补问题的一种全局收敛的显式光滑Newton方法   总被引:2,自引:0,他引:2  
本针对Po函数非线性互补问题,给出了一种显式光滑Newton方法,该方法将光滑参数μ进行显式迭代而不依赖于Newton方向的搜索过程,并在适当的假设条件下,证明了算法的全局收敛性。  相似文献   

10.
董丽  王洪芹  潘虹 《数学杂志》2015,35(6):1453-1460
本文研究了二阶锥规划问题.利用新的最小值函数的光滑函数,给出一个求解二阶锥规划的光滑牛顿算法.算法可以从任意点出发,在每一步迭代只需求解一个线性方程组并进行一次线性搜索.在不需要满足严格互补假设条件下,证明了算法是全局收敛和局部二阶收敛的.数值试验表明算法是有效的.  相似文献   

11.
《Quaestiones Mathematicae》2013,36(4):347-370
Abstract

In this note we obtain some extensions and an approximation of the Lyapunov convexity theorem by means of the bilinear integration of a set-valued function. The integration is performed successively with respect to a non-atomic, a direct sum and a Darboux vector measure. The necessary counterexamples are provided.  相似文献   

12.
The distinction between a priori and a posteriori knowledge has been the subject of an enormous amount of discussion, but the literature is biased against recognizing the intimate relationship between these forms of knowledge. For instance, it seems to be almost impossible to find a sample of pure a priori or a posteriori knowledge. In this paper, it will be suggested that distinguishing between a priori and a posteriori is more problematic than is often suggested, and that a priori and a posteriori resources are in fact used in parallel. We will define this relationship between a priori and a posteriori knowledge as the bootstrapping relationship. As we will see, this relationship gives us reasons to seek for an altogether novel definition of a priori and a posteriori knowledge. Specifically, we will have to analyse the relationship between a priori knowledge and a priori reasoning, and it will be suggested that the latter serves as a more promising starting point for the analysis of aprioricity. We will also analyse a number of examples from the natural sciences and consider the role of a priori reasoning in these examples. The focus of this paper is the analysis of the concepts of a priori and a posteriori knowledge rather than the epistemic domain of a posteriori and a priori justification.  相似文献   

13.
14.
15.
Matrices and operators of the formA –1 A * have received a certain amount of attention in recent years. Here some of the literature is surveyed and the caseA –1 A is studied for complex matrices withA denoting the transpose ofA. A generalization ofA –1 A is introduced.
Zusammenfassung Matrizen und Operatoren, die in der FormA –1 A * ausgedrückt werden können, sind in den letzten Jahren häufig studiert worden. Hier wird ein Ueberblick über Teil der relevanten Literatur gegeben und auch der FallA –1 A für komplexe Matrizen studiert, wobeiA die Transponierte vonA ist. Es wird auch eine Verallgemeinerung vonA –1 A eingeführt.


Dedicated to Eduard Stiefel by a long time admirer  相似文献   

16.
本文研究了有限群上的一个类函数.通过计算它和不可约特征标的内积,证明了它是特征标并且通过复群代数的中心的正则表示给出了它的一个模构造.  相似文献   

17.
Spreadsheets use a meaningful algebra-like notation which, research suggests, can support pupils in developing an understanding of variables. This paper discusses the activity of Year 8 pupils who were taught to name a column on a spreadsheet, and who were asked to reflect upon their activity in a stimulated recall interview. More specifically, it considers the pupils' understanding of notation, such as 'A2' and 'm', which they used when constructing spreadsheet formulae. It is suggested that experience of naming columns may help pupils to develop a clearer sense of the notation as a variable, and to make links between their spreadsheet activity and use of standard algebraic notation [1].  相似文献   

18.
Let M = (Mt,Ft) be a uniformly integrable continuous martingale with MO = 0. For1 5 p < cot we setIIMllBMO. = '3p II[E[IMoo ~ MTIplFT]]'/Pll.,where the supremum is taken over all stopping times T.Set BMO. = {M: IIMllBMO. < co}. It is well known that BMO. = BMO, (VI S p 5 q).F'urthermore, all 11.llBMO. norms are equivalent andIIi ~~if;llMllBMO. = SUP T P(T < co)i'where the supremum is taken over all stopping times T satisfying P(T < co) > 0. In the laterwe shall simply …  相似文献   

19.
20.
Let G be a group and τ e (G) the set of numbers of elements of G of the same order. In this paper, by τ e (G), we give a new characterization of A 5, where A 5 is the alternating group of degree 5. We get the theorem following: Theorem. Let G be a group, ${G\cong A_5}$ if and only if τ e (G) = τ e (A 5) = {1, 15, 20, 24}.  相似文献   

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