一簇非线性等式约束优化问题的过滤线搜索修正正割方法

本文提供了一簇新的过滤线搜索修正正割方法求解非线性等式约束优化问题.新算法簇的特点是:用修正正割算法簇中的一个算法获得搜索方向,回代线搜索技术得到步长,过滤准则用来决定是否接受步长,引入二阶校正技术减少不可行性并克服Maratos效应.在合理的假设条件下,分析了算法的总体收敛性.并证明了,通过附加二阶校正步,算法簇克服了Maratos效应,并二步Q-超线性收敛到满足二阶充分最优条件的局部解.数值结果表明了所提供的算法具有有效性.     

使用非单调线搜索正割方法解约束优化的整体收敛性

基于Powell和Yuan所建议的近似Fetcher罚函数作为函数使用单调线搜索的技术,本文提供了一类正割方法解约束优化。在合理的条件下,证明了所提供的算法的整体收敛性和收敛速率。     

一类求解非线性约束下的可行方向法

本文给出了一类关于非线性约束条件下的可行方向法。在较简单的假设之下,我们证明了算法具有全局收敛性。特别在本文中,我们利用此类算法和两个已有的线性约束下的梯度投影法导出了两个较简的非线性约束条件下收敛的梯度投影法。     

求解一类约束优化问题的Newton分裂算法

本文给出了求解一类约束优化问题的一个Newton分裂算法，并证明了算法的局部平方收敛性，该算法与已有算法相比，具有计算量小的特点，因而特别适合于求解大规模问题，为进一步降低算法的计算复杂性，我们结合Broyden算法，给出了两类Broyden类分裂算法。     

非线性约束优化问题的一个修正 Lagrangian 算法

基于一个含有控制参数的修正Lagrangian函数,该文建立了一个求解非线性约束优化问题的修正Lagrangian算法.在一些适当的条件下,证明了控制参数存在一个阀值,当控制参数小于这一阀值时,由这一算法产生的序列解局部收敛于问题的Kuhn-Tucker点,并且建立了解的误差上界.最后给出一些约束优化问题的数值结果.     

非线性等式与有界约束优化问题的正割算法

提出了结合仿射尺度技术的正割算法解非线性等式与有界约束优化问题. 在合理假设下, 证明了渐弱滤子线搜索方法可以保证新算法具有整体收敛性. 通过引入一个高阶修正方向, 克服Maratos效应的影响, 使得算法二步$q$-\!\!超线性收敛于最优点. 进一步地, 对算法进行修改, 使得新算法达到$q$-\!\!超线性收敛性.     

非线性约束优化问题的混合粒子群算法

把处理约束条件的一个外点方法和改进的粒子群优化算法相结合,提出了一种求解非线性约束优化问题的混合粒子群优化算法.该方法兼顾了粒子群优化和外点法的优点,对算法迭代过程中出现不可行粒子,利用外点法处理后产生可行粒子.数值实验表明了提出的新算法具有有效性、通用性和稳健性.     

非线性约束优化问题的一个新的全局收敛算法

对于非线性约束的优化问题.最近给出的各种SQP算法均采用罚函数技巧以保证算法的全局收敛性,因而都必须小心地调整惩罚参数。本文给出一个不依赖于惩罚参数、每步迭代的校正矩阵也不需正定且仍具有全局收敛性的SQP方法,而且罚函数形式简单、具有和约束函数同阶的光滑性.     

CONVERGENCE PROPERTIES OF IMPROVED SECANT METHODS WITH TRUST REGION MULTIPLIER

§ 1　 IntroductionWe consider the following equality contrained minimization problem:minf(x)s.t.c(x) =0 , (1 .1 )wheref :Rn→ R1 and c:Rn→ Rmare twice continuously differentiable.In[1 ] ,Fontecilla proposed the secant methods and proved their localq -superlineartwo-step convergence property under certain conditions.However,the global convergenceis not concerned in this paper,since Fontecilla did not discuss the important question ofensuring progress towards the solution of the problem(1 .1…     

A CLASS OF REDUCED GRADIENT METHODS FOR HANDLING OPTIMIZATION PROBLEMS WITH LINEAR INEQUALITY CONSTRAINTS

A class of reduced gradient methods for handling general optimization problems with linear equality and inequality constraints is suggested in this paper. Although a slack vector is introduced, the dimension of the problem is not increased, which is unlike the conventional way of transferring the inequality constraints into the equality constraints by introducing slack variables. When an iterate x(k) is not a K-T point of the problem under consideration, different feasible descent directions can be obtained by different choices of the slack vectors. The suggested method is globally convergent and the numerical experiment given in the paper shows that the method is efficient.     

求解非线性中立型延迟微分方程一类线性多步方法的收敛性

本文致力于带有Lagrang插值的一类线性多步法求解非线性中立型延迟微分方程的误差分析.证明了一个p′阶的线性多步方法配上一个q阶的Lagrang插值导致一个minf[p′,q 1]阶的E-(或EB-)收敛的非线性中立型延迟微分方程数值方法.     

A TRUST—REGION ALGORITHM FOR NONLINEAR INEQUALITY CONSTRAINED OPTIMIZATION

This paper presents a new trust-region algorithm for n-dimension nonlinear optimiza-tion subject to m nonlinear inequality constraints.Equivalent KKT conditions are derived,which is the basis for constructing the new algorithm.Global convergence of the algorithun to a first-order KKT point is eatablished under mild conditions on the trial steps.local quadratic convergence theorem is provcd for nondegenerate minimizer point.Numerical expcriment is prcsented to show the effectiveness of our approach.     

SEQUENTIAL SYSTEMS OF LINEAR EQUATIONS ALGORITHM FOR NONLINEAR OPTIMIZATION PROBLEMS-INEQUALITY CONSTRAINED PROBLEMS

AbstractIn this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations having a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQP type algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported.     

A TRUST REGION ALGORITHM FOR CONSTRAINED NONSMOOTH OPTIMIZATION PROBLEMS

1. Introductioncrust region methods are an hoportat class Of iterative wthods for solving nonlinearoptbozation problems, and have been developed rapidly in recent twenty years (see [1]--[9] 1 115] )[16] etc.). FOr nonsmooth optbozation problems, as early as in 1984, Y. Yuan [21 [3] prOPosed atrust region method for the composite function f(x) = h(g(x)), where h is convex and g E C';L. Qi and J. Sam [4] proposed an inexaCt trust region method for the general unconstrainednonsmooth optchatio…     

CONVERGENCE PROPERTIES OF A MODIFIED BFGS ALGORITHM FOR MINIMIZATION WITHARMIJO-GOLDSTEIN STEPLENGTHS

1.IntroductionAssumethatwearefindingtheminimizerofthefollowingunconstrainedoptimizationproblemminf(x),(1.1)acReandassumethecurrentpointisxk'TOcalculatexk 1fromxkbyalinesearchmethod,thefollowingiterationXk 1~Xk Akpk,k~1,2,'(1.2)isapplied.IntheBFGSal...     

A NEW SECANT METHOD FOR NONLINEAR LEAST SQUARES PROBLEMS

This paper is concerned with the solution of the nonlinear least squares problems. A new secant method is suggested in this paper, which is based on an affine model of the objective function and updates the first-order approximation each step when the iterations proceed. We present an algorithm which combines the new secant method with Gauss-Newton method for general nonlinear least squares problems. Furthermore, we prove that this algorithm is Q-superlinearly convergent for large residual problems under mild conditions.     

基于BDF的无约束优化方法的收敛性分析

1.介 绍 在上个世纪的七十年代末、八十年代初,基于常微分方程的优化方法或者说同伦方法是一类与拟牛顿法和共轭梯度法等我们所熟知的优化方法相竞争的重要方法[1-6,8,13,14,16].由于这类方法只是简单地利用现成的数值求解常微分方程的软件包,如CVODE[7]、LSODE[12],对同伦方程(一般是一个常微分方程的初值问题)进行计算,除了一些特殊的病态问题     

不等式约束优化一个新的SQP算法

本文提出了一个处理不等式约束优化问题的新的SQP算法．和传统的SQP算法相比,该算法每步只需求解一个仅含等式约束的子二次规划,从而减少了算法的计算工作量．在适当的条件下,证明算法是全局收敛的且具有超线性收敛速度．数值实验表明算法是有效的．