Inexact algorithm for continuous complementarity problems on measure spaces

In this paper, we discuss a type of complementarity problem posed over a measure space. We give some conditions under which there exists a solution for the problem and work toward a new inexact algorithm for its solution. A general convergence proof for this algorithm is given and the advantage of using this approach is discussed.The authors thank the referees for their helpful suggestions and comments.     

The nearest point problem in a polyhedral set and its extensions

In this paper we investigate the relationship between the nearest point problem in a polyhedral cone and the nearest point problem in a polyhedral set, and use this relationship to devise an effective method for solving the latter using an existing algorithm for the former. We then show that this approach can be employed to minimize any strictly convex quadratic function over a polyhedral set. Through a computational experiment we evaluate the effectiveness of this approach and show that for a collection of randomly generated instances this approach is more effective than other existing methods for solving these problems.     

On the cardinality of Urysohn spaces

Recently, in Cammaroto et al. (2013) [4] we obtained a generalization of the famous inequality established by A.V. Arhangel?ski? in 1969 for Hausdoff spaces. In this paper, following this line of research, we present a common variation of this inequality for Urysohn spaces by developing a Main Theorem for obtaining inequalities. In particular, we extend a 2006 inequality by Hodel for Urysohn spaces. Moreover, this extended inequality is used to analyze a result containing an increasing chain of spaces that satisfies the same cardinality inequality and this new result solves an open problem in Cammaroto et al. (2013) [4] for Urysohn spaces. This general theorem also provides a new cardinal inequality for Hausdorff spaces. The paper is concluded with some open problems.     

A class of operator equilibrium problems

In this paper, we consider a class of operator equilibrium problems (OEP for short) with operator solutions and derive a Minty type lemma for this class of problems. Further, using this lemma and KKM theorem, we establish some existence theorems for OEP. The theorems presented in this paper generalize, improve and unify many known results.     

Pompeiu Problem on Product of Heisenberg Groups

In this paper, we address the Pompeiu problem for a product of Heisenberg groups. We consider this problem both for cases of a ball and for a bidisk. Furthermore, we address this problem for a product of the Heisenberg group with Euclidean space.     

Asymptotic Behavior of Continuous Set-Indexed Martingales

In this paper, following the Knight's approach, we solve a convergence problem for set-indexed martingales. For this purpose, we first define a tightness criterion for set-indexed continuous processes. The core of this characterization is connected with a weaker definition of continuity and hence the use of the corresponding topology, and with the fact that indices take values in a semilattice of closed subsets. Then, we give an effective tightness criterion by means of an estimate for a majorizing measure defined on the space. We finally prove under this set-indexed framework a theorem similar to the Knight's.     

Sequential change-point detection for mixing random sequences under composite hypotheses

The problem of sequential detection of a change-point in the density function of one-dimensional distribution of observations from a mixing random sequence is considered when both before and after a change-point this density function belongs to a certain family of distributions, i.e. in the situation of composite hypotheses. A new quality criterion for change-point detection is proposed. The asymptotic a priori lower bound for this criterion is proved for wide class of methods of change-point detection. An asymptotically optimal method of change-point detection is proposed for which this lower bound is attained asymptotically. In particular, for the case of a simple hypothesis before a change-point, this method coincides with the generalized cumulative sums (CUSUM) method.      

非扩张映象有限族的公共不动点的隐式迭代方法

本文在实一致凸和q一致光滑Banach空间中研究了一类新的有限族非扩张映象的公共不动点的具误差和具扰动映射的隐式迭代程序并且得到了一些收敛性定理.特别地,获得了该隐式迭代程序强收敛性的充要条件.本文所得结论推广了文[1,2]中的相应结果.     

Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings

In this paper we propose a new implicit iteration scheme with perturbed mapping for approximation of common fixed points of a finite family of nonexpansive mappings. We establish some convergence theorems for this implicit iteration scheme. In particular, necessary and sufficient conditions for strong convergence of this implicit iteration scheme were obtained.     

一类一维的辐射流体力学方程组激波的存在性

该文主要讨论一维空间中一类辐射流体力学方程组的激波. 由Rankine-Hugoniot条件及熵条件得此问题可表述为关于辐射流体力学方程组带自由边界的初边值问题. 首先通过变量代换, 将其自由边界转换为固定边界, 然后研究关于此非线性方程组的一个初边值问题解的存在唯一性. 为此先构造了此问题的一个近似解, 然后分别通过Picard迭代与Newton迭代对此非线性问题构造近似解序列. 通过一系列估计与紧性理论得到此近似解序列的收敛性, 其极限即为原辐射热力学方程组的一个激波.     

A method for selecting a subset of alternatives for future decision making

In this paper we present an algorithm for finding a subset from a large number of alternatives. The criterion for selecting this subset is based on the assumption that ultimately one alternative will be chosen and implemented from this subset. Some areas of application for the subset selection techniques are presented. Extensions of this research are suggested.     

非光滑多目标规划的最优性

本文给出了一种新的右上导数定义,利用这一右上导数定义了几类广义凸性条件,进而讨论了非光滑多目标规划的最优性．包括Ｆｒｉｔｚ－Ｊｏｈｎ条件和Ｋｕｈｎ－Ｔｕｃｋｅｒ条件．     

On quadratic-like convergence of the means for two methods for simultaneous rootfinding of polynomials

Durand-Kerner's method for simultaneous rootfinding of a polynomial is locally second order convergent if all the zeros are simple. If this condition is violated numerical experiences still show linear convergence. For this case of multiple roots, Fraigniaud [4] proves that the means of clustering approximants for a multiple root is a better approximant for the zero and called this Quadratic-Like-Convergence of the Means.This note gives a new proof and a refinement of this property. The proof is based on the related Grau's method for simultaneous factoring of a polynomial. A similar property of some coefficients of the third order method due to Börsch-Supan, Maehly, Ehrlich, Aberth and others is proved.     

A second order scheme for the navier-stokes equations: stability and convergence

In this paper, a fully discretized projection method is introduced. It contains a parameter operator. Depending on this operator, we can obtain a first-order scheme, which is appropriate for theoretical analysis, and a second-order scheme, which is more suitable for actual computations. In this method, the boundary conditions of the intermediate velocity field and pressure are not needed. We give the proof of the stability and convergence for the first-order case. For the higher order cases, the proof were different, and we will present it elsewhere.

In a forthcoming article [7], we apply this scheme to the driven-cavity problem and compare it with other schemes     

有限族非扩张映象的公共不动点的具误差和具扰动映射的迭代程序

本文在实一致凸和q-一致光滑Banach空间中研究了一类新的有限族非扩张映象的公共不动点的具误差和具扰动映射的显式迭代程序并且得到了一些收敛性定理.特别地,获得了该显式迭代程序强收敛性的充要条件.本文所得到结果推广了文[1]中的相应结果.     

一般单调变分不等式的一个改进的预估-校正算法

最近何炳生等提出了解大规模单调变分不等式的一种预估-校正算法,然而,这个方法在计算每一个试验点时需要一次投影运算,因而计算量较大．为了克服这个缺点,我们提出了一个解一般大规模g-单调变分不等式的新的预估-校正算法,该方法使用了一个非常有效的预估步长准则,每个步长的选取只需要计算一次投影,这将大大减少计算量．数值试验说明我们的算法比最新文献中出现的投影类方法有效．     

Computing Optimal Distances to Pareto Sets of Multi-Objective Optimization Problems in Asymmetric Normed Lattices

Given a finite dimensional asymmetric normed lattice, we provide explicit formulae for the optimization of the associated (non-Hausdorff) asymmetric “distance” among a subset and a point. Our analysis has its roots and finds its applications in the current development of effective algorithms for multi-objective optimization programs. We are interested in providing the fundamental theoretical results for the associated convex analysis, fixing in this way the framework for this new optimization tool. The fact that the associated topology is not Hausdorff forces us to define a new setting and to use a new point of view for this analysis. Existence and uniqueness theorems for this optimization are shown. Our main result is the translation of the original abstract optimal distance problem to a clear optimization scheme. Actually, this justifies the algorithms and shows new aspects of the numerical and computational methods that have been already used in visualization of multi-objective optimization problems.

     

Banach空间中渐近非扩张非自身映射带误差Noor迭代的收敛性定理

本文主要对三个渐近非扩张非自身映射引入了一种新的投影型Noor迭代程序,并在一致凸Banach空间中给出了该Noor迭代序列的弱与强收敛性定理.我们的主要结果推广和改进了该领域许多近期的结果.     

Hilbert空间中关于松弛协强制映射的一类新的广义变分不等式组

在本文中,我们首先引入了一类新的关于松弛协强制映射的广义变分不等式组,通过用度量投影的方法,我们证明了这类广义变分不等式组解的存在性和唯一性.我们也建立了一类新的算法来逼近这一不等式组的解,本文的结果使得近期相关结果成为本文的特殊情况.     

Carleman estimate for a strongly damped wave equation and applications to an inverse problem

In this paper, we establish a Carleman estimate for a strongly damped wave equation in order to solve a coefficient inverse problems of retrieving a stationary potential from a single time‐dependent Neumann boundary measurement on a suitable part of the boundary. This coefficient inverse problem is for a strongly damped wave equation. We prove the uniqueness and the local stability results for this inverse problem. The proof of the results relies on Carleman estimate and a certain energy estimates for hyperbolic equation with strongly damped term. Moreover, this method could be used for a similar inverse problem for an integro‐differential equation with hyperbolic memory kernel. Copyright © 2012 John Wiley & Sons, Ltd.