1.

CONVERGENCE PROPERTIES OF MULTIDIRECTIONAL PARALLEL ALGORITHMS FOR UNCONSTRAINED MINIMIZATION





Chengxian Xu Yueting Yang《计算数学(英文版)》,2005年第23卷第4期


Convergence properties of a class of multidirectional parallel quasiNewton algorithmsfor the solution of unconstrained minimization problems are studied in this paper.At eachiteration these algorithms generate several different quasiNewton directions,and thenapply line searches to determine step lengths along each direction,simultaneously.Thenext iterate is obtained among these trail points by choosing the lowest point in the sense offunction reductions.Different quasiNewton updating formulas from the Broyden familyare used to generate a main sequence of Hessian matrix approximations.Based on theBFGS and the modified BFGS updating formulas,the global and superlinear convergenceresults are proved.It is observed that all the quasiNewton directions asymptoticallyapproach the Newton direction in both direction and length when the iterate sequenceconverges to a local minimum of the objective function,and hence the result of superlinearconvergence follows.

2.

线性互补问题的一种新Lagrange乘子法 被引次数：2





乌力吉 陈国庆《高等学校计算数学学报》,2004年第26卷第2期


A new multiplier method for solving the linear complementarity problem LCP(q, M) is proposed. Based on the Lagrangian of LCP(q,M) introduced here, we construct a new differentiable merit function θ(x,λ) which containing a multiplier vector λ and satisfying θ(x,λ) ≥ 0 and θ(x,λ) = 0 if and if only x solves LCP(q,M). A simple damped Newtontype algorithm which based on the merit function θ(x,λ) is presented. The main feature of the method is that the multiplier selfadjusting step accelerates the local convergence rate without losing global convergence. When M is the Pmatrix, the sequence {θ(x^k,λ^k)}where {(x^k,λ^k)} generated by the algorithm is globally linearly convergent to zero and convergent in finite number of iterations if the solution is nondegenerate. Numerical results suggest that the method is high efficient and promising.

3.

基于增广Lagrange函数的RQP方法 被引次数：3





王秀国 薛毅《计算数学》,2003年第25卷第4期


Recursive quadratic programming is a family of techniques developd by BartholomewBiggs and other authors for solving nonlinear programming problems.This paperdescribes a new method for constrained optimization which obtains its search directions from a quadratic programming subproblem based on the wellknown augmented Lagrangian function.It avoids the penalty parameter to tend to infinity.We employ the Fletcher‘s exact penalty function as a merit function and the use of an approximate directional derivative of the function that avoids the need toevaluate the second order derivatives of the problem functions.We prove that thealgorithm possesses global and superlinear convergence properties.At the sametime, numerical results are reported.

4.

A NEW TRUSTREGION ALGORITHM FOR NONLINEAR CONSTRAINED OPTIMIZATION





Lingfeng Niu Yaxiang Yuan《计算数学(英文版)》,2010年第1期


We propose a new trust region algorithm for nonlinear constrained optimization problems. In each iteration of our algorithm, the trial step is computed by minimizing a quadratic approximation to the augmented Lagrange function in the trust region. The augmented Lagrange function is also used as a merit function to decide whether the trial step should be accepted. Our method extends the traditional trust region approach by combining a filter technique into the rules for accepting trial steps so that a trial step could still be accepted even when it is rejected by the traditional rule based on merit function reduction. An estimate of the Lagrange multiplier is updated at each iteration, and the penalty parameter is updated to force sufficient reduction in the norm of the constraint violations. Active set technique is used to handle the inequality constraints. Numerical results for a set of constrained problems from the CUTEr collection are also reported.

5.

Properties of a family of merit functions and a merit function method for the NCP





Liyong Lu Zhenghai Huang and Shenglong Hu《高校应用数学学报(英文版)》,2010年第25卷第4期


A family of merit functions are proposed, which are the generalization of several existing merit functions. A number of favorable properties of the proposed merit functions are established. By using these properties, a merit function method for solving nonlinear complementarity problem is investigated, and the global convergence of the proposed algorithm is proved under some standard assumptions. Some preliminary numerical results are given.

6.

A HYBRID SMOOTHINGNONSMOOTH NEWTONTYPE ALGORITHM YIELDING AN EXACT SOLUTION OF THE P0LCP





ZhengHaiHuang LipingZhang JiyeHan《计算数学(英文版)》,2004年第22卷第6期


We propose a hybrid smoothingnonsmooth Newtontype algorithm for solving the P0 linear complementarity problem (P0LCP) based on the techniques used in the nonsmooth Newton method and smoothing Newton method. Under some assumptions, the proposed algorithm can find an exact solution of P0LCP in finite steps. Preliminary numerical results indicate that the proposed algorithm is promising.

7.

PIECEWISE LINEAR NCP FUNCTION FOR QP FREE FEASIBLE METHOD 被引次数：3





Pu Dingguo Zhou Yan《高校应用数学学报(英文版)》,2006年第21卷第3期


In this paper,a QPfree feasible method with piecewise NCP functions is proposed for nonlinear inequality constrained optimization problems.The new NCP functions are piece wise linearrational,regular pseudosmooth and have nice properties.This method is based on the solutions of linear systems of equation reformulation of KKT optimality conditions,by using the piecewise NCP functions.This method is implementable and globally convergent without assuming the strict complementarity condition,the isolatedness of accumulation points.Fur thermore,the gradients of active constraints are not requested to be linearly independent.The submatrix which may be obtained by quasiNewton methods,is not requested to be uniformly positive definite.Preliminary numerical results indicate that this new QPfree method is quite promising.

8.

Superlinear／Quadratic Onestep Smoothing Newton Methodf or P0NCP





LiPingZHANG JiYeHAN ZhengHaiHUANG《数学学报(英文版)》,2005年第21卷第1期


We propose a onestep smoothing Newton method for solving the nonlinear complementarity problem with P0function (P0NCP) based on the smoothing symmetric perturbed Fisher function(for short, denoted as the SSPFfunction). The proposed algorithm has to solve only one linear system of equations and performs only one line search per iteration. Without requiring any strict complementarity assumption at the P0NCP solution, we show that the proposed algorithm converges globally and superlinearly under mild conditions. Furthermore, the algorithm has local quadratic convergence under suitable conditions. The main feature of our global convergence results is that we do not assume a priori the existence of an accumulation point. Compared to the previous literatures, our algorithm has stronger convergence results under weaker conditions.

9.

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS





徐成贤 JongdeJ.L.《高校应用数学学报(英文版)》,1993年第8卷第2期


A Kind of direct methods is presented for the solution of optimal control problems with state constraints.These methods are sequential quadratic programming methods.At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and Linear approximations to constraints is solved to get a search direction for a merit function.The merit function is formulated by augmenting the Lagrangian funetion with a penalty term.A line search is carried out along the search direction to determine a step length such that the merit function is decreased.The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadrade programming methods.

10.

COMPOSITESTEP LIKE FILTER METHODS FOR EQUALITY CONSTRAINT PROBLEMS 被引次数：2





PuyanNie《计算数学(英文版)》,2003年第21卷第5期


In a compositestep approach, a step sk is computed as the sum of two components vk and hk. The normal component vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential component hk, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the compositestep like filter approach. That is, a step is tangential component hk if the infeasibility is reduced. Or else, sk is a compositestep composed of normal component Vk and tangential component hk.

11.

Thermospin effects in parallel coupled double quantum dots in the presence of the Rashba spinorbit interaction and Zeeman splitting





薛惠杰 吕天全 张红晨 尹海涛 催莲 贺泽龙《中国物理 B》,2012年第3期


The thermoelectric and the thermospin transport properties,including electrical conductivity,Seebeck coefficient,thermal conductivity,and thermoelectric figure of merit,of a parallel coupled doublequantumdot AharonovBohm interferometer are investigated by means of the Green function technique.The periodic Anderson model is used to describe the quantum dot system,the Rashba spinorbit interaction and the Zeeman splitting under a magnetic field are considered.The theoretical results show the constructive contribution of the Rashba effect and the influence of the magnetic field on the thermospin effects.We also show theoretically that material with a high figure of merit can be obtained by tuning the Zeeman splitting energy only.

12.

A SPECIAL KIND OF NONOSCILLATORY SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS





蒲富全《应用数学学报(英文版)》,1988年第1期


In this note the nonoscillatory property of y"+p(x)y=0,where p(x) is a periodic pulse function,is considered.Sufficient condition for guaranteeing nonscillation is obtained.We compare the result with obtained by applying Adamov's theorem.

13.

求解非线性规划的原始对偶内点法(英文)





张珊 姜志侠《东北数学》,2008年第24卷第3期


In this paper, we propose a primaldual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.

14.

Onestep estimation for varying coefficient models





TANG Qingguo & WANG Jinde Department of Mathematics Nanjing University Nanjing 210093 China Institute of Sciences PLA University of Science and Technology Nanjing 210007 China《中国科学A辑(英文版)》,2005年第48卷第2期


A onestep method is proposed to estimate the unknown functions in the varying coefficient models, in which the unknown functions admit different degrees of smoothness. In this method polynomials of different orders are used to approximate unknown functions with different degrees of smoothness. As only one minimization operation is employed, the required computation burden is much less than that required by the existing twostep estimation method. It is shown that the onestep estimators also achieve the optimal convergence rate. Moreover this property is obtained under conditions milder than that imposed in the twostep estimation method. More importantly, as only one minimization operation is employed, the full asymptotic properties, not only the asymptotic bias and variance, but also the asymptotic distributions of the estimators can be derived. The asymptotic distribution results will play a key role for making statistical inference.

15.

A NEW SMOOTHING EQUATIONS APPROACH TO THE NONLINEAR COMPLEMENTARITY PROBLEMS 被引次数：1





ChangfengMa PuyanNie GuopingLiang《计算数学(英文版)》,2003年第21卷第6期


The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a new smoothing approximation function. Global and local superlinear convergence results of the algorithm are obtained under suitable conditions. Numerical experiments confirm the good theoretical properties of the algorithm.

16.

NEW NUMERICAL METHOD FOR VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND IN PIEZOELASTIC DYNAMIC PROBLEMS





丁皓江 王惠明 陈伟球《应用数学和力学(英文版)》,2004年第25卷第1期


The elastodynamic problems of piezoelectric hollow cylinders and spheres under radial deformation can be transformed into a second kind Volterra integral equation about a function with respect to time, which greatly simplifies the solving procedure for such elastodynamic problems. Meanwhile, it becomes very important to find a way to solve the second kind Volterra integral equation effectively and quickly. By using an interpolation function to approximate the unknown function, two new recursive formulae were derived, based on which numerical solution can be obtained step by step. The present method can provide accurate numerical results efficiently. It is also very stable for long time calculating.

17.

A QP FREE FEASIBLE METHOD 被引次数：21





DingguoPu YanZhou HaiyanZhang《计算数学(英文版)》,2004年第22卷第5期


In [12], a QP free feasible method was proposed for the minimization of a smooth function subject to smooth inequality constraints. This method is based on the solutions of linear systems of equations, the reformulation of the KKT optimality conditions by using the FischerBurmeister NCP function. This method ensures the feasibility of all iterations. In this paper, we modify the method in [12] slightly to obtain the local convergence under some weaker conditions. In particular, this method is implementable and globally convergent without assuming the linear independence of the gradients of active constrained functions and the uniformly positive definiteness of the submatrix obtained by the Newton or Quasi Newton methods. We also prove that the method has superlinear convergence rate under some mild conditions. Some preliminary numerical results indicate that this new QP free feasible method is quite promising.

18.

Primary vertex reconstruction based on the Kalman filter technique at BESⅢ





徐敏 何康林 张子平 王贻芳 边渐鸣 傅成栋 黄彬 季晓斌 孙胜森 严亮 张建勇《中国物理 C》,2010年第34卷第1期


Primary vertex reconstruction is crucial to estimate the beam profile in collision experiments. We study the principle of an iterative process, called the Kalman filter method, and apply it to primary vertex reconstruction at BESⅢ. A Newton procedure to find the zero point of the distance function＇s gradient is used for primary vertex finding in 3dimensional space. Results are obtained based on raw data at BESⅢ.

19.

Wigner Distribution Function and Husimi Function of a Kind of Squeezed Coherent State





FAN HongYi LIU ShuGuang《理论物理通讯》,2007年第47卷第3期


We find a new xparameter squeezed coherent state （p, q）κ representation, which possesses wellbehaved features, i.e., its Wigner function＇s marginal distribution in the ＂qdirection＂ and in the ＂pdirection＂ is the Gauss/an form exp（κ（q＇  q）2}, and exp{（p＇  p）2/κ}, respectively. Based on this, the Husimi function of（p, q）κ is also obtained, which is a Gauss/an broaden version of the Wigner function. The （P, q）κ state provides a good representative space for studying various properties ot the Husimi operator.

20.

ON SEMILOCAL CONVERGENCE OF INEXACT NEWTON METHODS





Xueping Guo《计算数学(英文版)》,2007年第25卷第2期


Inexact Newton methods are constructed by combining Newton＇s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton＇s method, we obtain a different NewtonKantorovich theorem about Newton＇s method. When the iterative method for solving the Newton equations is specified to be the splitting method, we get two estimates about the iteration steps for the special inexact Newton methods.
