A UNIFIED APPROACH TO THE METHOD OF GRADIENT PROJECTION WITH ARBITRARY INITIAL POINT

In this paper,we present a family of gradient projection method with arbitrary initialpoint.The formula of search direction in the method is unitary.The convergent conditions ofthe method are given.When the initial point is feasible,the family of the method contains severalknown algorithms.When the initial point is infeasible,the method is exactly that given in[6].Finally,we give a new method which has global convergence property.     

A GENERALIZED GRADIENT METHOD FOR NONLINEAR CONSTRAINTS AND ITS CONVERGENT PROPERTIES

ＡＧＥＮＥＲＡＬＩＺＥＤＧＲＡＤＩＥＮＴＭＥＴＨＯＤＦＯＲＮＯＮＬＩＮＥＡＲＣＯＮＳＴＲＡＩＮＴＳＡＮＤＩＴＳＣＯＮＶＥＲＧＥＮＴＰＲＯＰＥＲＴＩＥＳＧＡＯＺｉｙｏｕ（ＮｏｒｔｈｅｒｎＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１０００４４，...     

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…     

OPTIMAL VALUE FUNCTIONS IN MATHEMATICAL PROGRAMMING AND CONVERGENCE FOR GRADIENT PROJECTION METHOD

ＯＰＴＩＭＡＬＶＡＬＵＥＦＵＮＣＴＩＯＮＳＩＮＭＡＴＨＥＭＡＴＩＣＡＬＰＲＯＧＲＡＭＭＩＮＧＡＮＤＣＯＮＶＥＲＧＥＮＣＥＦＯＲＧＲＡＤＩＥＮＴＰＲＯＪＥＣＴＩＯＮＭＥＴＨＯＤ￥ＷＡＮＧＣｈａｎｇｙｕ；ＺＨＡＯＦｕａｎ（ＩｎＳｔｉｔｕｔｅｏｆＯＲ，Ｑｕ...     

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.     

A SUPERLINEAR CONVERGENT FEASIBLE METHOD FOR NONLINEAR PROGRAMMING WITH NONLINEAR CONSTRAINTS

ＡＳＵＰＥＲＬＩＮＥＡＲＣＯＮＶＥＲＧＥＮＴＦＥＡＳＩＢＬＥＭＥＴＨＯＤＦＯＲＮＯＮＬＩＮＥＡＲＰＲＯＧＲＡＭＭＩＮＧＷＩＴＨＮＯＮＬＩＮＥＡＲＣＯＮＳＴＲＡＩＮＴＳ￥ＧＡＯＺｉｙｏｕ；ＨＥＧｕｏｐｉｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈ...     

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.     

CONVERGENCE PROPERTIES OF PROJECTED GRADIENT METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR CONVEX CONSTRAINED OPTIMIZATION

1. IntroductionGiven some function f(x): Wu - FI over a nonempty closed set n C W", one is interestedin solving the fOllowing optimization problem with constraints amin f(x)s.t. x E n (1.1)where f(x): Q C Wu - FI is twice continuously differentiable. This problem has receivedconsiderable attention extensively. The linear constrained case where n is a polyhedron is ofspecial inferest. Recently, there are quite a few articles proposing projected gradient methodsto solve the problem (see, fo…     

A VARIATION OF GOLDFARB'S METHOD FOR LINEARLY CONSTRAINED OPTIMIZATION PROBLEMS AND ITS SUPERLINEAR CONVERGENCE RATE

1.IntroductionRosen'sgradientprojectionmethodisaveryinterestingtechniqueinoptimization(see[1,2]),butitsglobalconvergenceisalong-standingopenproblemintheliterature.Thefirstconvergentversionwasfoundbyp.l.k[3].ButPolak'sversionistoocomplicated.Du[4]alsofoundasimplerconvergentversionbydeletingPolak'sspecialprocedure.CombiningRosen'smethodwithvariablemetricmethods,Goldfarb[sl,MurtaghandSargentl'lobtainedtwoefficientalgorithms.Theconvergenceofsuchalgorithmsisstillanopenproblem.However,severalcon…     

A NEW SUFFICIENT CONDITION FOR THE CONVERGENCE OF THE DFP ALGORITHM WITH WOLFE LINE SEARCH

ＡＮＥＷＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＦＯＲＴＨＥＣＯＮＶＥＲＧＥＮＣＥＯＦＴＨＥＤＦＰＡＬＧＯＲＩＴＨＭＷＩＴＨＷＯＬＦＥＬＩＮＥＳＥＡＲＣＨ￥ＸＵＤａｃｈｕａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＱｕｆｕＮｏｒｍａｌＵｎｉｖ...     

A ROBUST SQP METHOD BASED ON A SMOOTHING APPROXIMATE PENALTY FUNCTION FOR INEQUALITY CONSTRAINED OPTIMIZATION

1 IntroductionConsider the following inequality constrained optiInization problem:Inin f(x)xeRn(1)s.t. g(x) 5 0where f: R1'-R, g: R"-Rm are cofltinuousIy differentiable functions.SQP method for soIving problem(1) is to gellerate a sequence {xk} converging…     

A NEW APPROACH ON IDENTIFICATION OF BOUNDARY PARAMETER FOR A TWODIMENSIONAL DIFFUSION SYSTEM

This paper presents a new approach of the boundary parameter identification of adiffusion system.The system model is governed by a two-dimensional parabolic problem,which involves an unknown boundary parameter.Identifiability of the boundary parameterand the new approach are discussed briefly,which show that the new approach can overcomenot only the ill-posedness of the nonlinear output least square method but also the difficultyof numerical computation of the nonlinear output least square estimate due to the existenceof the local minima of the performance functional,Finally,some numerical examples aregiven.     

AN SQP METHOD BASED ON SMOOTHING PENALTY FUNCTION FOR NONLINEAR OPTIMIZATION WITH INEQUALITY CONSTRAINT

1 IntroductionIn tabs paper, we consider the following nonlinear optbostion problem:where j: Re - R, g: Re - Re are continuously ~ntiable functinns. SoP method forproblem (1) generates a sequence of points which converges to a K--T point of problem (1)through the following iterate formulaxk 1 = x* adds (2)adhere da is the solution of the following quadratic Prograrxuning problemin which Bh is a sylnlnetric positive deflate lllatris and A* is a stepsise obtained by some lineseaxch to redu…     

A general iterative method of fixed points for equilibrium problems and optimization problems

The purpose of this paper is to present a general iterative scheme as below:

一种求解动态多峰优化问题的Memetic粒子群算法

很多现实的优化问题往往是动态和多峰的, 这就需要优化算法既能够发现尽可能多的最优解, 同时还要追踪到这些最优解在动态环境中的变化轨迹. 为了解决这种动态多峰优化问题, 本文提出了一种Memetic粒子群优化算法. 在提出的算法中, 利用一种新的species构造方法来保证其能够发现不同最优解所在搜索区域, 利用一种适应性的局域搜索算子来增强species追踪到最优解的能力, 利用重新初始化策略来进一步改善算法在动态多峰环境中的性能. 通过对一组标准动态测试函数--移动峰问题的仿真实验来检验所提出的 MPSO算法在求解动态多峰优化问题的有效性.     

A MULTISTEP CHARACTERISTIC FINITE DIFFERENCE METHOD FOR TWO-DIMENSIONAL NONLINEAR CONVECTION-DIFFUSION PROBLEMS

1.IntroductionItiswellknowthattheconvection-dictionproblemsareakindofveryimportalprob-lems,particularlylthenonlinearconvection-diffusionproblexns.Inthepaper[1],asinglestepcharacteristicflutedmerencemethodisgivenforsolvingtwcadimensionalnonlinearconvection-dilhaionproblemswiththeconvectivecoefficientsdominating.HereweshallgiveamultistepcharactersticamrencemethodbasedonthelinearandquadraticinterpolationsforsolvingtwcadAnensionalnonlinearconvection-~ionproblemsinordertoincreasetheaccuracyofapprot…     

基于目标希望水平的多目标决策新方法

本文提出一种基于目标希望水平的多目标决策新方法，该方法按照实际决策思维方式构造产生非劣解的辅助问题，充分考虑决策人在决策过程中的交互要求，通过决策人对目标希望水平的确定或修正获取有用的偏好信息，简单、实用，易于在计算机上实现。文中给出的若干定理保证了决策方法的有效性。     

一种新颖的花朵授粉优化算法及收敛性分析

针对现有花朵授粉算法存在易早熟、寻优精度不高、搜索效率低下等问题,研究设计了一种改进的花朵授粉算法。该算法利用逻辑自映射函数对花粉粒进行混沌扰动,使缺乏变异机制的花粉粒集具有较强的自适应能力,有效地防止了算法后期最优解趋同的现象。利用变换算子对搜索空间进行动态收缩,使算法在寻优过程中保持较高的种群多样性,降低算法陷入局部极值的概率,从而提高算法的搜索效率和寻优精度。同时,结合花朵授粉的生物学特征,从机理上描述了改进后算法的具体实现步骤,对算法的收敛性和寻优性能进行了详细的剖析,并采用实数编码的方法分析了算法的收敛性,给出了算法的生物学模型和理论基础。实验结果表明,改进后的算法具有较好的性能。     

求解N-车探险问题的离散水波优化算法

N-车探险问题是一类NP-hard离散优化问题,针对该问题,首次提出一种融合局部搜索的离散水波优化算法。结合该问题等价于置换排序的特性,设计基于置换序列的编码方式;利用反转、移动、交换等操作重新定义传播、折射和碎浪算子;开发基于插入邻域的局部搜索策略,以增强水波优化算法的局部搜索能力。最后,利用实验设计探讨关键参数对算法性能的影响。基于14个标准问题的测试结果表明：所提方法的寻优精度、稳定性等整体优于标准水波优化算法、粒子群算法、烟花算法和启发式算法H1~H4;与离散水波优化算法相比,基于禁忌搜索的变邻域搜索算法用至少66.6倍的计算时间得到了最大相对偏差比为0.017的寻优精度。结果表明,离散水波优化算法能在较短时间内获得较满意的解。