半无限极大极小问题的全局收敛方法

利用广义伪方向导数，在较弱的条件下，给出了半无限极大极小问题（P）的全局收敛性理论算法模型；利用离散策略给出了问题（P）全局收敛的可实现算法．数值结果表明本文给出的可实现算法是有效的．     

一般约束极大极小问题的一个有效的近似解法

一般约束极大极小问题的一个有效的近似解法唐焕文，张立卫，王云诚（大连理工大学应用数学系，辽宁，１１６０２４）．摘要＊从共扼的观点出发，导出了极大熵函数，给出了处理一般约束极大极小问题的一个有效的近似方法—极大熵方法，并在较弱的条件下，证明了算法的收敛...     

半无限极小极大问题的信赖域算法

本文以处理半无限最优化问题的一般技巧,将一类针对有限极小极大问题的信赖域算法推广到半无限极小极大问题。并证明了新建算法的全局收敛性和超线性收敛性。     

求解约束极大极小问题的一种熵函数法

１引言熵函数法的原始思想源于Ｋｒｅｉｓｓｅｌｍｅｉｅｒ和Ｓｔｅｉｎｈａｕｓｅｒ于１９７９年发表的文［１］．由于使用该方法容易编制可以求解多类优化问题的通用软件,并在具有某种凸性的情况下都能求得满足工程精度要求的解,因而受到国内外工程技术人员的喜爱,进入八十年代以来,该方法被广泛地应用于结构优化和工程设计等领域［２－５］．近年来,熵函数法在求解约束和无约束极大极小问题、线性规划以及半无限规划等问题的算法研究中,也取得了一些很好的成果［６－９］带有等式或不等式约束的极大极小问题是一类具有广泛代表性的…     

极大极小问题极大熵方法的收敛性

本文给出了极大极小问题的一种概念性的极大熵方法，并在较弱的条件下，证明了这种方法的收敛性。     

极大熵方法与指数罚函数

就非线性极大极小问题，阐明了极大熵方法与指数罚方法的关系．通过分析相关Ｈｅｓｓｉａｎ阵的条件数，对二者进行了对比．     

求解约束极小极大问题的一种K─S函数的近似迭代法

借助于极大熵方法和逼近法，给出了一种求解约束极小极大问题的K－S函数近似迭代法，同时讨论算法的有关收敛性．     

非线性极大极小问题一个新的QP-free算法

本文研究非线性无约束极大极小优化问题. QP-free算法是求解光滑约束优化问题的有效方法之一,但用于求解极大极小优化问题的成果甚少.基于原问题的稳定点条件,既不需含参数的指数型光滑化函数,也不要等价光滑化,提出了求解非线性极大极小问题一个新的QP-free算法.新算法在每一次迭代中,通过求解两个相同系数矩阵的线性方程组获得搜索方向.在合适的假设条件下,该算法具有全局收敛性.最后,初步的数值试验验证了算法的有效性.     

一种新的求解带约束的有限极大极小问题的精确罚函数

提出了一种新的精确光滑罚函数求解带约束的极大极小问题．仅仅添加一个额外的变量,利用这个精确光滑罚函数,将带约束的极大极小问题转化为无约束优化问题． 证明了在合理的假设条件下,当罚参数充分大,罚问题的极小值点就是原问题的极小值点．进一步,研究了局部精确性质．数值结果表明这种罚函数算法是求解带约束有限极大极小问题的一种有效算法．     

约束极小极大问题的一种既约梯度近似法

利用极大熵方法及有关逼近结果，使之与既约梯度法结合，提出了一种求解极小极大非线性规划问题的近似法，并证明了算法的有关收敛性结果。     

一种基于TOPSIS思想的改进灰色关联法及其在方案评估中的应用

提出了一种基于TOPSIS思想的改进灰色关联法,方法采用了TOPSIS思想,通过标准化处理,能够将灰色关联法给出的评估结果转换为,TOPSIS方法所要用到的与最优/最劣解的距离,从而给出一个稳定的评估结果,弥补了传统灰色关联法受全局极值影响大的缺点.经实例分析证明,方法可以应用于方案评估中,并能够得出可行、稳定、科学的评估结果.     

无约束最优化锥模型拟牛顿信赖域方法的收敛性(英)

本文研究无约束最优化雄模型拟牛顿信赖域方法的全局收敛性．文章给出了确保这类方法全局收敛的条件．文章还证明了，当用拆线法来求这类算法中锥模型信赖域子问题的近似解时，确保全局收敛的条件得到满足     

Rare-Event Simulation of Non-Markovian Queueing Networks Using a State-Dependent Change of Measure Determined Using Cross-Entropy

A method is described for the efficient estimation of small overflow probabilities in nonMarkovian queueing network models. The method uses importance sampling with a state-dependent change of measure, which is determined adaptively using the cross-entropy method, thus avoiding the need for a detailed mathematical analysis. Experiments show that the use of rescheduling is needed in order to get a significant simulation speedup, and that the method can be used to estimate overflow probabilities in a two-node tandem queue network model for which simulation using a state-independent change of measure does not work well.     

A limited memory descent Perry conjugate gradient method

In this work, we present a new limited memory conjugate gradient method which is based on the study of Perry’s method. An attractive property of the proposed method is that it corrects the loss of orthogonality that can occur in ill-conditioned optimization problems, which can decelerate the convergence of the method. Moreover, an additional advantage is that the memory is only used to monitor the orthogonality relatively cheaply; and when orthogonality is lost, the memory is used to generate a new orthogonal search direction. Under mild conditions, we establish the global convergence of the proposed method provided that the line search satisfies the Wolfe conditions. Our numerical experiments indicate the efficiency and robustness of the proposed method.     

Variable metric relaxation methods,part II: The ellipsoid method

The deepest, or least shallow, cut ellipsoid method is a polynomial (time and space) method which finds an ellipsoid, representable by polynomial space integers, such that the maximal ellipsoidal distance relaxation method using this fixed ellipsoid is polynomial: this is equivalent to finding a linear transforming such that the maximal distance relaxation method of Agmon, Motzkin and Schoenberg in this transformed space is polynomial. If perfect arithmetic is used, then the sequence of ellipsoids generated by the method converges to a set of ellipsoids, which share some of the properties of the classical Hessian at an optimum point of a function; and thus the ellipsoid method is quite analogous to a variable metric quasi-Newton method. This research was supported in part by the F.C.A.C. of Quebec, and the N.S.E.R.C. of Canada under Grant A 4152.     

Fixed-point iterations in determining a Tikhonov regularization parameter in Kirsch’s factorization method

Kirsch’s factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. The mathematical basis of this method is given by the far-field equation, which is a Fredholm integral equation of the first kind in which the data function is a known analytic function and the integral kernel is the measured (and therefore noisy) far-field pattern. We present a Tikhonov parameter choice approach based on a fast fixed-point iteration method which constructs a regularization parameter associated with the corner of the L-curve in log-log scale. The performance of the method is evaluated by comparing our reconstructions with those obtained via the L-curve and we conclude that our method yields reliable reconstructions at a lower computational cost.     

蕴含权重的偏序集多准则决策法

针对偏序集方法不能解决含有权重的多准则决策问题,提出一种“隐式”赋权的偏序决策方法。首先将含有m个方案和n个准则的决策问题表示成偏序集,之后按权重由大到小的顺序,对准则进行逐步相加形成n个新的准则,得到一个新的偏序集。根据偏序集间的包含关系,证明了新偏序集不仅蕴含了权重信息,而且比初始偏序集有更强的排序能力。结果表明,该法在应用中仅需获取权重排序信息,无需精确权重,适用于权重难以确定的多准则决策问题。以三峡库区水质评价为例,例子表明新方法明显优于原有的偏序决策方法,能够对13个方案进行聚类和排序,而原有方法在该例中几乎难以应用。     

Three-point finite-difference schemes, Padé and the spectral Galerkin method. I. One-sided impedance approximation

A method for calculating special grid placement for three-point schemes which yields exponential superconvergence of the Neumann to Dirichlet map has been suggested earlier. Here we show that such a grid placement can yield impedance which is equivalent to that of a spectral Galerkin method, or more generally to that of a spectral Galerkin-Petrov method. In fact we show that for every stable Galerkin-Petrov method there is a three-point scheme which yields the same solution at the boundary. We discuss the application of this result to partial differential equations and give numerical examples. We also show equivalence at one corner of a two-dimensional optimal grid with a spectral Galerkin method.

     

偏微分方程的区间小波自适应精细积分法

利用插值小波理论构造了拟Shannon区间小波,并结合外推法给出了一种求解非线性常微分方程组的时间步长自适应精细积分法,在此基础上构造了求解非线性偏微分方程的区间小波自适应精细积分法（AIWPIM）．数值结果表明,该方法在计算精度上优于将小波和四阶Runge-Kutta法组合得到的偏微分方程的数值求解方法,而计算量则相差不大．该文方法通过Burgers方程给出,但适用于一般情形．     

A generalized Newton method for absolute value equations associated with second order cones

In this paper, we introduce the absolute value equations associated with second order cones (SOCAVE in short), which is a generalization of the absolute value equations discussed recently in the literature. It is proved that the SOCAVE is equivalent to a class of second order cone linear complementarity problems (SOCLCP in short). In particular, we propose a generalized Newton method for solving the SOCAVE and show that the proposed method is globally linearly and locally quadratically convergent under suitable assumptions. We also report some preliminary numerical results of the proposed method for solving the SOCAVE and the SOCLCP, which show the efficiency of the proposed method.