GLOBAL CONVERGENCE OF THE DAI-YUAN CONJUGATE GRADIENT METHOD WITH PERTURBATIONS

In this paper, the authors propose a class of Dai-Yuan （abbr. DY） conjugate gradient methods with linesearch in the presence of perturbations on general function and uniformly convex function respectively. Their iterate formula is xk＋1 = xk ＋ αk（sk ＋ ωk）, where the main direction sk is obtained by DY conjugate gradient method, ωk is perturbation term, and stepsize αk is determined by linesearch which does not tend to zero in the limit necessarily. The authors prove the global convergence of these methods under mild conditions. Preliminary computational experience is also reported.     

Global Convergence Property of Conjugate Gradient Methods for Optimization

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利用共轭梯度法分析有限矩形波导相控阵

对于大阵一般把它作为无限阵来分析,求得其输入阻抗和其它参数。无限阵可以用周期结构进行严格求解,因为采用周期结构,实际上只要求解一个单元室就可以,这样问题相对来说就简单多了。但对于小阵采用无限周期结构误差较大,因此必须采用有限阵的分析方法。有限阵分析方法常常因为问题太复杂,受计算机容量和速度的限制,只能求解较小的阵。为此本文介绍了一种带有无限接地板的有限阵分析方法,这种方法是采用模匹配法严格地求解边值问题,因此求解精度比较高。另外,本文在公式推导、简化以及计算方法上采取了以下措施,即在求解过程中,本文利用列文的方法,将四重积分化为二重积分,计算量可大大减少。同时,本文还利用Toeplitz性质,将计算量进一步减少。Toeplitz性质和共轭梯度法的结合,将储存空间大大减少,使得对较大的有限阵分析成为可能,这使得本方法在工程实际中具有更大的使用价值。     

Global Convergence of the Conjugate Descent Method Under a kind of Inexact Line Search Conditions

1　 IntroductionWe consider the unconstrained optimizatoin problem( P) :minf( x) ,x∈ Rnwhere f:Rn→R is continuously differentiable and its gradient f( x) is denoted by g( x) .The conjugate gradient method is useful for calculating local unconstrained optimizationproblem of differentiable functions of many variables,it has the following form:xk 1 =xk λkdk ( 1 .1 )dk=-gk,k =1-gk βkdk- 1 ,k 2 ( 1 .2 )whereλk is a step-size obtained by a line search,andβk is a parameter,which can beobtaine…     

A NEW CONJUGATE GRADIENT METHOD AND ITS GLOBAL CONVERGENCE PROPERTIES

1.Intr0ductionConsidertheunconstrainedminimizationproblemminf(x),xER",(1)wheref:R"-R1isacontinuouslydifferentiablefunction.Inthispaperwerestrictourselvestostudyingtheconjugategradientmethodoftheformwherex1isagiveninitialp0int,dkisthesearchdirection,crkistllesteplengtllalongdk,gk=g(xk)isthegradientoffatxkandPkisasuitablescalar.Thewell-knownibrmulasforgkaretheFletcherandReeves(FR)formulaReceivedN0vemberRevisedMarchl4,l997.*Thisresearchissupp0rtedbytheNati0nalNa1lraIScienceF0undationofChi…     

CONVERGENCE PROPERTIES OF CONJUGATEGRADIENT METHODS WITH STRONG WOLFE LINESEARCH

1.IntroductionWeconsidertheconjugategradientmethodsfortheunconstrainedoptimizationproblemdinf(x),wheref:R"-- FI,fECI.Thenewiterativeisgivenbywherethesearchdirectiondhisdefinedbyhereukbeingparameters.Somewell-knownchoicesforohareItismeaningfultoinvestigatetheglobalconvergencepropertiesoftheabovementionedconjugategradientmethodsappliedtononconvexfunctions.In12],Powellprovedglobalcon...:::::f::ti;::,2:trbi?:v::C:fh:;::?:oe:vaec:f:n:::i:r:1l:fl:llw:::s?'\t-n::ti,5':::::::iPowell'sconvergencere…     

二维发汗控制方程的直线解法及其收敛性

对二维发汗控制方程建立了直线解法,可用任何解常微分方程组的数值方法求解。对固定边界（非烧蚀）和活动边界（烧蚀）情形分别进行讨论。在某些假定下给出了直线法的收敛性。     

A CLASS OF REVISED BROYDEN ALGORITHMS

In this paper, we discuss the convergence of the Broyden algorithms with revised search direction. Under some inexact llne searches, we prove that the algorithms are globally convergent for continuously differentiable functions and the rate of convergence of the algorithms is one-step superlinear and n-step second-order for uniformly convex objective functions.     

非线性随机延迟微分方程Euler-Maruyama方法的收敛性

首先利用附近已有节点上的值通过插值对延迟项进行数值逼近,这是一种崭新的尝试;然后针对较一般情形下的一类非线性随机延迟微分方程初值问题,得到了带线性插值的Euler-Maruyama方法在均方意义下是收敛的理论结果,它部分推广了已有文献中的相关结论。     

GLOBAL CONVERGENCE PROPERTIES OF THREE-TERM CONJUGATE GRADIENT METHOD WITH NEW-TYPE LINE SEARCH

In this paper, a new Wolfe-type line search and a new Armijo-type line search are proposed, and some global convergence properties of a three-term conjugate gradient method with the two line searches are proved.     

THE CONVERGENCE OF BROYDEN ALGORITHMSWITHOUT CONVEXITY ASSUMPTION

1.IatroductionWeknowthatthevariablemetricalgorithms,suchastheBroydenalgorithms[1],areveryusefulandefficientmethodsforsolvingthenonlinearprogrammingproblem:min{f(x);xERn}.(1.1)Withexactlinesearch,Powelll2]provedthattherateofconvergenceofthesealgorithmsisone-stepsuperlinearfortheuniformlyconvexobjectivefunction,andifthepoiedsgivenbythesealgorithmsareconvergeal,PnandYul3]provedthattheyaregloballyconvergelitforthecolltinuousdifferentiablefunction.Withoutexactlinesearchseveralresultshavebeenobtai…     

A New Convergence Result of Gauss－Newton Methods for the Complementarity Problem

1　 IntroductionL et F∶Rn→Rnbe continuously differentiable.The nonlinear complementarity problem isto find a solution of the following system of equations and inequalities:x 0 ,F( x) 0 ,x TF( x) =0or,equivalently,xi 0 ,Fi( x) 0 ,xi Fi( x) =0 ,　 i =1,… ,nWe denote this problem by NCP( F) .When F is an affine function and is of the formF( x) =Mx qM is an n× n real matrix and q∈ Rn,the complementarity problem is referred to as thelinear complementarity,denoted by L CP( M,q) .N…     

Alternative Theorems and Sufficient Conditions of Global Convergence for a Class of Feasible Direction Algorithms

In this paper,two alternative theorems which differ from Theorem 10.2.6 in [1] andTheorem 1 in [3] are presented for a class of feasible direction algorithms.On the basis of alternativetheorems,furthermore,two sufficient conditions of global convergence of this class of algorithms areobtained.     

EQUILIBRIUM ALGORITHMS WITH NONMONOTONE LINE SEARCH TECHNIQUE FOR SOLVING THE TRAFFIC ASSIGNMENT PROBLEMS

This paper presents a unified bination algorithms （such as FrankWolfe problems. Global convergence results are framework of the nonmonotone convex comAlgorithm） for solving the traffic assignment established under mild conditions. The line search procedure used in our algorithm includes the nonmonotone Armijo rule, the non- monotone Goldstein rule and the nonmonotone Wolfe rule as special cases. So, the new algorithm can be viewed as a generalization of the regular convex combination algorithm.     

On the Convergence of a New Hybrid Projection Algorithm

For unconstrained optimization, a new hybrid projection algorithm is presented m the paper. This algorithm has some attractive convergence properties. Convergence theory can be obtained under the condition that Δ↓f（x） is uniformly continuous. If Δ↓f（x） is continuously differentiable pseudo-convex, the whole sequence of iterates converges to a solution of the problem without any other assumptions. Furthermore, under appropriate conditions one shows that the sequence of iterates has a cluster-point if and only if Ω＊ ≠ θ. Numerical examples are given at the end of this paper.     

单线列车运行调整的梯度搜索算法仿真与研究

列车运行调整的优化是一个非常复杂的问题,需考虑的因素很多,很难给出一个完美的优化模型。根据单线列车运行调整的特点,建立了单线列车运行图的离散事件拓扑图模型,提出了＂调整运行图综合满意度＂作为运行调整的目标,并进一步论证了＂调整运行图综合满意度＂函数的单调递减特性;提出了冲突树的概念和梯度搜索算法的算法原理及搜索步骤,并实例进行仿真。仿真结果表明,该算法模型在实际运行过程中的具有较好的优化性和有效性。

Abstract：

The optimization of railway rescheduling is a very complex issue, many factors should to be taken into account, and it’s difficult to give a perfect optimization model. A discrete event topologic diagram model was derived according to the characteristics of the single-track railway diagram, and the ＂comprehensive satisfaction of the adjusted train diagram＂ was proposed as the target of the railway rescheduling, then the monotonically decreasing characteristic of the target function was demonstrated. The concept of conflict tree was developed and the principle and steps of the gradient search algorithm based on the DET model were given and simulated. The simulation results show that this algorithm has better adaptability and effectiveness in practical application.     

基于虚拟组分的热物理性质计算方法库

提出的热物理性质计算方法库与文献[1]中的基础物性数据计算方法库组成了一个内置于原油蒸馏过程模型与在线优化软件中的物性数据计算方法库.本文介绍了方法库中的部分计算方法,并通过实例应用,取得了良好的效果.     

Global Convergence Analysis of Non-Crossover Genetic Algorithm and Its Application to Optimization

Selection, crossover, and mutation are three main operators of the canonical genetic algorithm (CGA). This paper presents a new approach to the genetic algorithm. This new approach applies only to mutation and selection operators. The paper proves that the search process of the non-crossover genetic algorithm (NCGA) is an ergodic homogeneous Markov chain. The proof of its convergence to global optimum is presented. Some nonlinear multi-modal optimization problems are applied to test the efficacy of the NCGA. NP-hard traveling salesman problem (TSP) is cited here as the benchmark problem to test the efficiency of the algorithm. The simulation result shows that NCGA achieves much faster convergence speed than CGA in terms of CPU time. The convergence speed per epoch of NCGA is also faster than that of CGA.     

Global Convergence of Adaptive Generalized Predictive Controller Based on Least Squares Algorithm

Some papers on stochastic adaptive control schemes have established convergence algorithm using a least-squares parameters. With the popular application of GPC, global convergence has become a key problem in automatic control theory. However, now global convergence of GPC has not been established for algorithms in computing a least squares iteration. A generalized model of adaptive generalized predictive control is presented. The global convergebce is also given on the basis of estimating the parameters of GPC by least squares algorithm.     

Convergence and stability of the Newton-Like algorithm with estimation error in optimization flow control

The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed.The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed.Based on the optimization theory,a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained.Furthermore,even when this sufficient condition doesn't hold,this algorithm can also converge,provided a modified step size,and an attraction region is obtained.Based on Lasalle's invariance principle applied to a suitable Lyapunov function,the dynamic system described by this algorithm is proved to be global stability if the error is zero.And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence.All trajectories ultimately converge to the equilibrium point.