The Global Convergence of Self-Scaling BFGS Algorithm with Nonmonotone Line Search for Unconstrained Nonconvex Optimization Problems

The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is convex （or even uniformly convex）. We propose to solve unconstrained nonconvex optimization problems by a self-scaling BFGS algorithm with nonmonotone linear search. Nonmonotone line search has been recognized in numerical practices as a competitive approach for solving large-scale nonlinear problems. We consider two different nonmonotone line search forms and study the global convergence of these nonmonotone self-scale BFGS algorithms. We prove that, under some weaker condition than that in the literature, both forms of the self-scaling BFGS algorithm are globally convergent for unconstrained nonconvex optimization problems.     

第Ⅲ类非自共轭锥上的Gamma函数

本文将Ｇａｍｍａ函数及Ｓｉｅｇｅｌ积分推广到一般的第Ⅲ类非自共轭锥上,作为其应用,显式给出了以这些锥为底的管状域（也称第一类Ｓｉｅｇｅｌ域）的Ｃａｕｃｈｙ－Ｓｚｅｇｏ核和形式Ｐｏｉｓｓｏｎ核。关键词     

COUPLED FIXED POINTS OF SKEW INCREASING OPERATORS AND APPLICATIONS

1Intr0ducti0nIllthisPaPerwestudythefordpointsandcouPledfiXedpointsofskewincreasing0PeratorsandtheiraPplicaion.LetXbeaBanachsPaCcwithapartialorderingintr0ducedbythcc0neK-LctF:X-Xbean0peraorinX.FiscaJledinCreasingifF2SFgf0raJl2Sy.Asiswellkllown,inthetheorerns0fhapointforincreasingoPerbo,thereisaninterestinginterreboi0nbetweenPr0pertiesofKandF,thatisThoorem1l1I'I2ILetXbeaBanachpee,partiaJlyorderedbythecolleKGX.Let[a,b]beanordeintervalandF:[a,b]- [a,b]increasin.ThenFhasabop0intif0…     

第四类超Cartan域的Bergman核函数

显式给出了第四类超Cartan域的Bergman核函数及其全纯自同构群．     

Anisotropy of sound velocity for a new PbB4O7 crystal as determined by the laser ultrasonic technique

4 O₇ crystal is a new nonlinear optical crystal. For the first time the anisotropy of the velocities of its longitudinal and surface acoustic waves (SAWs) are determined by laser ultrasonic technique. The velocities of surface waves for X-, Y-, and Z-cut crystals are also calculated. The theoretical calculations of slowness curves are in good agreement with experimental results. The SAW slowness curve is elliptical for Y- or Z-cut crystal wafers, and circular for an X-cut wafer. Received: 27 January 1997/Accepted: 30 July 1997     

模拟回火马尔可夫链蒙特卡罗全波形分析方法

针对传统的全波形分析方法不能快速自动处理全波形数据的缺点,提出了一种模拟回火马尔可夫链蒙特卡罗全波形分析法,用于求解全波形数据中的波峰数和峰值位置等参量.该方法采用Metropolis更新策略求解波峰数量和噪声两个参量,以达到快速求解的目的;而峰值位置和波峰幅值则采用改进的模拟回火策略求解,通过添加的主动干预回火步骤实现对参量更新过程的有效探测,以满足对速度或运算收敛性的要求.模拟回火马尔可夫链蒙特卡罗全波形分析方法以马尔可夫算法为基础,仍保持马氏链的收敛性,从而保证本方法具有良好的鲁棒性,实现对全波形数据的自动化处理.     

火焰原子吸收光谱法测定粮食中的铜

碳化酸溶消解试样,用火焰原子吸收光谱法测定三种粮食作物中的铜.回收率:99.5%-107.0%.方法快速、简便、准确度高.     

基于多元线性阵列探测器的快速光声层析成像

报道了一种基于相控聚焦的多元线性阵列探测器进行快速光声层析成像的方法和装置,并实现了模拟组织的光声层析成像。实验中采用波长为532nm脉宽为7ns的倍频Q-YAG激光器作为激发光源。多元线性阵列探测器由320个振元组成,采用相控聚焦的方法成像,每次由11个振群的探测器接受信号并合并1路,一幅图像由64路这样的信号组成。实验结果能够正确反映样品中的光学吸收分布。与现有的方法比较,本系统具有快速方便的特点,它有望成为一种组织功能在体成像的新方法,发展成为一种低成本的实用的临床诊断装置。     

1，3-二甲基尿嘧啶二聚体的飞行时间质谱裂解规律研究

采用不同进样方式、不同电子轰击能量和不同反应气压力测定了1,3 二甲基尿嘧啶二聚体(DMUD) 的4个立体异构体A、B、C、D的化学电离(CI)和电子轰击电离(EI)飞行时间质谱.不同方式所测得的CI谱结 果一致,4个异构体出现了强度不同的准分子离子峰(m/z=281),由此推断它们结构之间的相对稳定性次序为: B(trans syn)>D(cis syn)>A(trans anti)>C(cis anti).这一结论被低能量(25eV)电子轰击的EI谱所证实, 并且与合成产物的比例相吻合.EI谱用任何方式测谱均不出现分子离子峰(m/z=280),而出现其单体离子(m/z =140)且为基峰。给出了DMUD的飞行时间质谱裂解途径,同时对CI谱的裂解碎片进行了细致的讨论.