求解界约束优化的一种新的非单调谱投影梯度法

本文给出求解界约束优化问题的一种新的非单调谱投影梯度算法. 该算法是将谱投影梯度算法与Zhang and Hager [SIAM Journal on Optimization,2004,4（4）：1043-1056]提出的非单调线搜索结合得到的方法. 在合理的假设条件下,证明了算法的全局收敛性.数值实验结果表明,与已有的界约束优化问题的谱投影梯度法比较,利用本文给出的算法求解界约束优化问题是有竞争力的.     

Wolfe步长规则下约束优化问题的共轭梯度投影算法

本文研究了约束优化问题min x∈Ωf(x).利用共轭梯度算法与GLP梯度投影思想相结合的方法,构造了一个新的共轭梯度投影算法,并在Wolfe线搜索下获得了该算法的全局收敛性结果.     

A SPARSE SUBSPACE TRUNCATED NEWTON METHOD FOR LARGE-SCALE BOUND CONSTRAINED NONLINEAR OPTIMIZATION

In this paper we report a sparse truncated Newton algorithm for handling large-scale simple bound nonlinear constrained minimixation problem. The truncated Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At each iterative level, the search direction consists of three parts, one of which is a subspace truncated Newton direction, the other two are subspace gradient and modified gradient directions. The subspace truncated Newton direction is obtained by solving a sparse system of linear equations. The global convergence and quadratic convergence rate of the algorithm are proved and some numerical tests are given.     

A NEW ADAPTIVE SUBSPACE MINIMIZATION THREE-TERM CONJUGATE GRADIENT ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

A new adaptive subspace minimization three-term conjugate gradient algorithm with nonmonotone line search is introduced and analyzed in this paper.The search directions are computed by minimizing a quadratic approximation of the objective function on special subspaces,and we also proposed an adaptive rule for choosing different searching directions at each iteration.We obtain a significant conclusion that the each choice of the search directions satisfies the sufficient descent condition.With the used nonmonotone line search,we prove that the new algorithm is globally convergent for general nonlinear functions under some mild assumptions.Numerical experiments show that the proposed algorithm is promising for the given test problem set.     

求解随机凸规划概率约束问题的对偶算法

1引言随机规划中的概率约束问题在工程和管理中有广泛的应用.因为问题中包含非线性的概率约束,它们的求解非常困难.如果目标函数是线性的,问题的求解就比较容易.给出了一个求解随机线性规划概率约束问题的综述.原-对偶算法和切平面算法是比较有效的.在本文中,我们讨论随机凸规划概率约束问题:     

A REVISED CONJUGATE GRADIENT PROJECTION ALGORITHM FOR INEQUALITY CONSTRAINED OPTIMIZATIONS

A revised conjugate gradient projection method for nonlinear inequality constrained optimization problems is proposed in the paper, since the search direction is the combination of the conjugate projection gradient and the quasi-Newton direction. It has two merits. The one is that the amount of computation is lower because the gradient matrix only needs to be computed one time at each iteration. The other is that the algorithm is of global convergence and locally superlinear convergence without strict complementary condition under some mild assumptions. In addition the search direction is explicit.     

RECONDITIONED SPECTRAL PROJECTED GRADIENT METHOD ON CONVEX SETS

The spectral gradient method has proved to be effective for solving large-scale uncon-strained optimization problems.It has been recently extended and combined with theprojected gradient method for solving optimization problems on convex sets.This combi-nation includes the use of nonmonotone line search techniques to preserve the fast localconvergence.In this work we further extend the spectral choice of steplength to accept pre-conditioned 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 discussimplementation details for solving large-scale problems.     

一个求解无约束优化问题的条件预优共轭梯度法

1 引言 考虑无约束最优化问题minf(x)(1.1)     

线性约束规划拓广的既约梯度法及其收敛性

本文首先给出由线性等式和不等式以及部分变量非负组成的约束集的一个新的转轴运算。它是以往转轴运算的推广。然后,以此为基础,建立该约束条件下的非线性规划的一个拓广的既约梯度法,它是既约梯度法的广泛推广和改进。算法不需增加任何松驰变量,以致提高问题的维数,扩大问题的规模;方法直接对原问题进行求解。本文算法对一般线性约束规划具有广泛的实用性,其处理技巧带有普遍意义。在非退化假设下,本文算法具有全局收敛性。     

一类新的共轭梯度法

本文提出了一类新的共轭梯度法，在算法的迭代过程中，迭代方向保持下降性，并在一类非精确性搜索条件下证明了其全局收敛性。     

一个共轭梯度方法全局收敛性的判别准则

本文建立了一个共轭梯度方法全局收敛性的判别准则,基于这一准则证明了一类三参数共轭梯度法的全局收敛性及DY方法的一个变形的全局收敛性.     

求解大规模极大极小问题的光滑化三项共轭梯度算法

基于指数罚函数,对最近提出的一种求解无约束优化问题的三项共轭梯度法进行了修正,并用它求解更复杂的大规模极大极小值问题.证明了该方法生成的搜索方向对每一个光滑子问题是充分下降方向,而且与所用的线搜索规则无关.以此为基础,设计了求解大规模极大极小值问题的算法,并在合理的假设下,证明了算法的全局收敛性.数值实验表明,该算法优于文献中已有的类似算法.     

预处理CG算法解油藏模拟问题的有效性比较

1引言 在大型科学和工程计算问题的实际应用中，经常会遇到求解除椭圆型或抛物线型偏微分方程问题。经差分法或有限元方法离散化后得到一个大型稀疏线性方程组。本文比较了几     

A NEW INEXACT SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM

This paper represents an inexact sequential quadratic programming (SQP) algorithm which can solve nonlinear programming (NLP) problems. An inexact solution of the quadratic programming subproblem is determined by a projection and contraction method such that only matrix-vector product is required. Some truncated criteria are chosen such that the algorithm is suitable to large scale NLP problem. The global convergence of the algorithm is proved.     

AN EFFECTIVE SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM FOR NONLINEAR OPTIMIZATION PROBLEMS

In this paper,a new globally convergent algorithm for nonlinear optimization prablems with equality and inequality constraints is presented. The new algorithm is of SQP type which determines a search direction by solving a quadratic programming subproblem per itera-tion. Some revisions on the quadratic programming subproblem have been made in such a way that the associated constraint region is nonempty for each point x generated by the algorithm, i. e. , the subproblems always have optimal solutions. The new algorithm has two important properties. The computation of revision parameter for guaranteeing the consistency of quadratic sub-problem and the computation of the second order correction step for superlinear convergence use the same inverse of a matrix per iteration, so the computation amount of the new algorithm will not be increased much more than other SQP type algorithms; Another is that the new algorithm can give automatically a feasible point as a starting point for the quadratic subproblems pe     

由FR共轭梯度法控制的两类优化算法的全局收敛性

１引言 考虑无约束优化问题其中ｆ：Ｒｎ→Ｒ是一阶可微函数．求解（１）的非线性共轭梯度法具有如下形式：其中ｇｋ＝　ｆ（ｘｋ）,ａｋ是通过某种线搜索获得的步长,纯量βｋ的选取使得方法（２）—（３）在ｆ（ｘ）是严格凸二次函数且采用精确线搜索时化为线性共轭梯度法［１］．比较常见的βｋ的取法有Ｆｌｅｔｃｈｅｒ－Ｒｅｅｖｅｓ（ＦＲ）公式［２］和Ｐｏｌａｋ－Ｒｉｂｉｅｒｅ－Ｐｏｌｙａｋ（ＰＲＰ）公式［３－４］等．它们分别为其中　　　取欧几里得范数．对于一般非线性函数,ＦＲ方法具有较好的理论收敛性［５－６］,而…     

A PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING

The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interior-point method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.     

约束极小极大问题的一种既约梯度近似法

利用极大熵方法及有关逼近结果，使之与既约梯度法结合，提出了一种求解极小极大非线性规划问题的近似法，并证明了算法的有关收敛性结果。     

A RESTARTING DIRECTION FOR THE CONJUGATE GRADIENT METHOD

The main purpose of this paper is to provide a restarting direction for improving on the standard conjugate gradient method.If a drastic non-quadratic behaviour of the objective function is observed in the neighbour of xk,then a restart should be done.The scaling symmetric rank-one update with Davidon's optimal criterion is applied to generate the restarting direction.It is proved that the conjugate gradient method with this strategy retains the quadratic termination.Numerical experiments show that it is successful.     

在Goldstein搜索下一类共轭梯度法的全局收敛性

本文证明了文「１」提出的一类共轭梯度法在Ｇｏｌｄｓｔｅｉｎ非精确线性搜索下具有全局收敛性。