积分—水平集总极值算法的另一实现途径

在（１）中提出了一个积分－水平集求总极值的概念性算法及Ｍｏｎｔｅ－Ｃａｒｌｏ随机投点的实现途径，并在不少实际问题中得到了很好的应用。但这一实际算法的收敛性是个未解决的问题。本文给出了另一实现途径，并证明了收敛性。从而从理论上证明了这一实现算法一定能求到总极值和总极值点，数值试验结果也支持这一理论结果。     

计算Adomian多项式的新算法

本文给出了一个计算Adomian多项式的新算法,并将其用于求微分方程的近似 解.我们的算法比原有算法效率高,且易于在计算机上实现.我们在Maple中实现了这一 算法,并通过30多个微分方程的求解验证了新算法的有效性.     

最小树问题的全部解

<正> 以某些实际问题(如管道设计、通讯网建设等)为背景,图论中的最小树问题引起人们的广泛兴趣.自从 Kruskal 提出三种基本的构造法以后,各种算法实现途径相继出现,使这一问题得到完满的解决.然而,实际问题往往不能满足于求出一个最小树,而希望兼顾其它目标,在若干最小树中进行再选择.这就要求我们讨论最小树问题的全部解.在已有文献中,求全部支撑树已有较成熟的算法,尤其是文献[4]提供的算法可以将全部支撑树按权的大小依次列出.从理论上说,可以认为这些结果已经包含了求全部最小树问题.作为另一种途径,本文将着重讨论最小树问题全部解的性质,并由此建立求全部解的广探法(求全部支撑树的 Mayeda-Seshu 算法的推广).     

变差积分型约束总极值问题的不连续罚途径

结合积分途径运用不连续精确罚函数来求解全局约束最小化问题,进一步,提出了约束变差积分的一般形式并证明了其分析性质,同时也给出并证明了其全局最优性条件,并由此设计了一个新算法.基于Monte-Carlo模拟技术,运用交叉熵方法和重要样本实现了该算法,数值实验也说明了这个新算法是有效的.     

极小化加权总完工时间的分批排序问题

本文讨论了分批排序中极小化加权总完工时间的两个问题.就所有工件的加工时间都相等这一特殊情况,分别给出两个算法,并证明了算法的最优性.     

基于改进蚁群算法的侦察无人机航路规划与实现

文章针对侦察无人机航路规划这一问题,分析了影响航路规划的因素,构建了航路规划的模型.结合侦察无人机航路规划的特点与模型,论证了基于蚁群算法求解的理由与优点,并对蚁群算法的初始信息素强度与启发因子进行了改进.最后以岛屿进攻战役这一特定作战任务为例,利用MATLAB实现了侦察多目标时的航路规划问题.     

Minimum Global Height支撑树及相关问题

本文研究了两个组合优化问题:minimum g1obal height支撑树和minimum aveageheight支撑树问题.利用3SAT问题的时间复杂性,本文证明了这两个问题都是NP-hard的,并分别给出了一个算法,即（mgh）-算法和（mah）-算法.在非负网络中,这两个算法的时间复杂性都为O（n3）.利用第一个问题的复杂性,本文证明了minimum height支撑树问题也是NP-hard的,从而纠正了有关文献中的一个错误结论.     

供给总量限定需求区间约束型运输问题——时限费用优化模型与算法

本文目的是为建立与运输问题有关的决策支持系统提供方便.本文建立了供给总量限定需求区间约束型运输问题的对时限与费用两个目标进行优化的多目标规划模型,给出了求解模型的算法,并举例说明了算法的应用.该算法能求得问题的最优解,并具有易于编程实现、收敛性好等优点.数值实验表明该算法有较高的计算效率,可用于求解某些类型的指派问题.     

介质导电率成像数值反演的正则化方法

磁共振技术(MREIT)是一种新的医学成像技术,它利用介质内部的部分磁场信息来重建介质内部的导电率.本文对调和Bz反演算法,提出了利用样条插值函数来处理误差输入数据的正则化方法,并给出了正则化方法的误差估计,在此基础上,我们还考虑了调和Bz算法对多个导电率异常的算法实现,检验了该方法对误差输入数据借助于正则化方法可能达到的空间分辨率,本文的工作为调和Bz算法利用实测的误差数据提供了一条可行的途径.     

一类非线性两级整数规划问题的全局优化方法

本文研究了整数规划连续化的途径,对一类非线性两级整数规划问题的上级规划连续化以后采用模拟退火算法;其对应的下级规划问题采用离散搜索法求解,从而给出了求解一类非线性两级整数规划问题的一种全局优化算法,并通过算例验证了该算法是有效的.     

一种修正的求总极值的积分—水平集方法的实现算法收敛性

1978年,郑权等提出了一个积分型求总极值的概念性算法及Monte-Carlo随机投点的实现算法,给出了概念性算法的总极值存在的充分必要条件,但是其实现算法收敛性仍未解决,1986年,张连生等给出离散均值－水平集的实现算法,并证明了它的收敛性。本文给出修正的积分－水平集方法,用一致分布搂九值积分逼近水平集构造实现算法,并证明了算法的收敛性。     

Generalized primal-relaxed dual approach for global optimization

A generalized primal-relaxed dual algorithm for global optimization is proposed and its convergence is proved. The (GOP) algorithm of Floudas and Visweswaran (Refs. 1–2) is shown to be a special case of this general algorithm. Within the proposed framework, the algorithm of Floudas and Visweswaran (Refs. 1–2) is further extended to the nonsmooth case. A penalty implementation of the extended (GOP) algorithm is studied to improve its efficiency.     

A ROBUST TRUST REGION ALGORITHM FOR SOLVING GENERAL NONLINEAR PROGRAMMING

1. Introductioncrust region methods are iterative. As a strategy of globalization, the trust region approach was introduced into solving unconstrained optimization and proved to be efficient androbust. An excellent survey was given by Mor6(1983). The associated research with trustregion methods for unconstrained optimization can be found in Fletcher(1980), Powell(1975),Sorensen(1981), Shultz, Schnabel and Byrd(1985), Yuan(1985). The solution of the trust region subproblem is still an activ…     

求解带二次约束的非凸二次规划的一种分支定界算法

本文提出了一种求解带二次约束和线性约束的二次规划的分支定界算法.在算法中,我们运用Lipschitz条件来确定目标函数和约束函数的在每个n矩形上的上下界,对于n矩形的分割,我们采用选择n矩形最长边的二分法,同时我们采用了一些矩形删除技术,在不大幅增加计算量的前提下,起到了加速算法收敛的效果.从理论上我们证明了算法的收敛性,同时数值实验表明该算法是有效的.     

On the eigenvalues of the saddle point matrices discretized from Navier–Stokes equations

In this paper, we proposed an implementation of stochastic perturbation of reduced gradient and bisection (SPRGB) method for optimizing a non-convex differentiable function subject to linear equality constraints and non-negativity bounds on the variables. In particular, at each iteration, we compute a search direction by reduced gradient, and optimal line search by bisection algorithm along this direction yields a decrease in the objective value. SPRGB method is desired to establish the global convergence of the algorithm. An implementation and tests of SPRGB algorithm are given, and some numerical results of large-scale problems are presented, which show the efficient of this approach.     

Convergence Properties of the DFP Algorithm for Unconstrained Optimization

In this article, the convergence properties of the DFP algorithm with inexact line searches on uniformly convex functions are investigated. An inexact line search is proposed and the global convergence and superlinear convergence of the DFP algorithm with this line search on uniformly convex functions are proved.     

Use of the Minimum-Norm Search Direction in a Nonmonotone Version of the Gauss-Newton Method

In this work, a new stabilization scheme for the Gauss-Newton method is defined, where the minimum norm solution of the linear least-squares problem is normally taken as search direction and the standard Gauss-Newton equation is suitably modified only at a subsequence of the iterates. Moreover, the stepsize is computed by means of a nonmonotone line search technique. The global convergence of the proposed algorithm model is proved under standard assumptions and the superlinear rate of convergence is ensured for the zero-residual case. A specific implementation algorithm is described, where the use of the pure Gauss-Newton iteration is conditioned to the progress made in the minimization process by controlling the stepsize. The results of a computational experimentation performed on a set of standard test problems are reported.     

Preconditioned Spectral Projected Gradient Method on Convex Sets

The spectral gradient method has proved to be effective for solving large-scale unconstrained optimization problems. It has been recently extended and combined with the projected gradient method for solving optimization problems on convex sets. This combination includes the use of nonmonotone line search techniques to preserve the fast local convergence. In this work we further extend the spectral choice of steplength to accept preconditioned directions when a good preconditioner is available. We present an algorithmthat combines the spectral projected gradient method with preconditioning strategies toincrease the local speed of convergence while keeping the global properties. We discuss implementation details for solving large-scale problems.     

A line search trust-region algorithm with nonmonotone adaptive radius for a system of nonlinear equations

In this paper, a trust-region procedure is proposed for the solution of nonlinear equations. The proposed approach takes advantages of an effective adaptive trust-region radius and a nonmonotone strategy by combining both of them appropriately. It is believed that selecting an appropriate adaptive radius based on a suitable nonmonotone strategy can improve the efficiency and robustness of the trust-region frameworks as well as decrease the computational cost of the algorithm by decreasing the required number subproblems that must be solved. The global convergence and the local Q-quadratic convergence rate of the proposed approach are proved. Preliminary numerical results of the proposed algorithm are also reported which indicate the promising behavior of the new procedure for solving the nonlinear system.     

一类连续函数模拟退火算法及其收敛性分析

高维连续函数的全局优化问题普遍存在于计算生物学、计算化学等领域．针对这类问题和现有连续函数模拟退火算法的某些不足,本文给出了一类改进的模拟退火算法．采用一种简单的方法证明了算法的全局收敛性．数值结果表明,对于高维连续函数,该算法能够快速有效地收敛到全局最优点,比较了两种新解产生方法的试验结果。