一个解大规模无约束优化问题的全局梯度法(英文)

本文提出一种新的解大规模无约束优化问题的全局收敛的梯度法.新算法沿着负梯度方向选择步长,而初始步长根据目标函数的海赛矩阵的近似数量矩阵来确定.理论上证明了新算法产生的点列的每个聚点都是稳定的,数值试验表明新算法是可靠且有效的.     

A General Iterative Method for Solving Constrained Convex Minimization Problems

It is well known that the gradient-projection algorithm plays an important role in solving minimization problems. In this paper, we will use the idea of regularization to establish a general method so that the sequence generated by the general method can be strongly convergent to a minimizer of constrained convex minimization problems, which solves a variational inequality under suitable conditions.     

极大极小问题的广义投影算法

研究了无约束极大极小问题.通过引入一个可微的辅助函数,利用广义投影技术产生下降搜索方向,结合Armjio非精确线搜索建立了一个广义梯度投影算法.在初始点任意的条件下,证明了算法的全局收敛性.     

A Quasi-Newton Method with Memory for Unconstrained Function Minimization

A quasi-Newton method for unconstrained function minimizationis described which requires very little additional programmingto that required for the memory gradient method of Miele &Cantrell and which usually converges in far fewer iterations.The new method is essentially that of Fletcher & Powellwith memory; computational experience shows that it can be moreefficient than the method of Fletcher & Powell.     

The Substitution Secant/Finite Difference Method for Large Scale Sparse Unconstrained Optimization

This paper studies a substitution secant/finite difference （SSFD） method for solving large scale sparse unconstrained optimization problems. This method is a combination of a secant method and a finite difference method, which depends on a consistent partition of the columns of the lower triangular part of the Hessian matrix. A q-superlinear convergence result and an r-convergence rate estimate show that this method has good local convergence properties. The numerical results show that this method may be competitive with some currently used algorithms.     

The 2-Coordinate Descent Method for Solving Double-Sided Simplex Constrained Minimization Problems

This paper considers the problem of minimizing a continuously differentiable function with a Lipschitz continuous gradient subject to a single linear equality constraint and additional bound constraints on the decision variables. We introduce and analyze several variants of a 2-coordinate descent method: a block descent method that performs an optimization step with respect to only two variables at each iteration. Based on two new optimality measures, we establish convergence to stationarity points for general nonconvex objective functions. In the convex case, when all the variables are lower bounded but not upper bounded, we show that the sequence of function values converges at a sublinear rate. Several illustrative numerical examples demonstrate the effectiveness of the method.     

Globally Convergent Variable Metric Method for Nonconvex Nondifferentiable Unconstrained Minimization

A special variable metric method is given for finding the stationary points of locally Lipschitz continuous functions which are not necessarily convex or differentiable. Time consuming quadratic programming subproblems do not need to be solved. Global convergence of the method is established. Some encouraging numerical experience is reported.     

A New Direction Set Method for Unconstrained Minimization without Evaluating Derivatives

A new direction set method for unconstrained minimization withoutevaluating derivatives is presented. The algorithm can be regardedas an application to function minimization of Jacobi's methodfor determining the eigenvalues and eigenvectors of a real symmetricmatrix. Numerical results are presented, illustrating the performanceof the new algorithm on well-known test problems; a comparisonwith other methods is also given.     

Globally Convergent Variable Metric Method for Convex Nonsmooth Unconstrained Minimization1

A special variable metric method is given for finding minima of convex functions that are not necessarily differentiable. Time-consuming quadratic programming subproblems do not need to be solved. Global convergence of the method is established. Some encouraging numerical experience is reported.     

求解l1极小化问题的Bregman迭代算法

在Tikhonov正则化方法的基础上将其转化为一类l1极小化问题进行求解,并基于Bregman迭代正则化构建了Bregman迭代算法,实现了l1极小化问题的快速求解.数值实验结果表明,Bregman迭代算法在快速求解算子方程的同时,有着比最小二乘法和Tikhonov正则化方法更高的求解精度.     

Heuristic Methods for Solving Large Scale Network Routing Problems: The Telpaking Problem

An approach to a large scale network routing problem with nonlinear cost function is described, along with an example of its application. The approach to the problem involves a multistage construction process. This approach is applied to the telpaking problem. Results are obtained in applying this method to a 53 node sample problem.     

解大系统稳定性的积分方程法

本文通过分解积分方程组，并建立积分方程法比较原理，化大系统为低维系统，进而讨论了带时滞的时变大系统的稳定性，给出了新的结果，这一方法也可以用来讨论其它类型大系统的稳定性问题．     

Adaptive Global Algorithm for Solving Box-Constrained Non-convex Quadratic Minimization Problems

Journal of Optimization Theory and Applications - In this paper, we propose a new adaptive method for solving the non-convex quadratic minimization problem subject to box constraints, where the...     

求解无约束优化问题的一个秩一适定方法

在本文中,我们给出一个求解无约束优化问题的秩一适定方法,该方法具有下述较好性质:校正矩阵是对称正定的;在适当条件下,对非凸函数拥有全局收敛性.我们还给出数值检验结果.     

On Convergence Properties of Algorithms for Unconstrained Minimization

Suppose F is a convex function on R" for which there is a sequenceof points on which the function values are bounded below andthe gradients converge to zero. Is it possible that F is unboundedbelow? The answer, perhaps surprisingly, is yes for n > 1.     

无约束不可微观划的信赖域算法

提出了一种易实施的求无约束不可微规划的信赖域算法,并在一定条件下证明了该算法所产生的点列的任何聚点都是原问题的稳定点。     

基于非拟牛顿方法无约束最优化问题的全局收敛性

In this paper, the non-quasi-Newton's family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton's family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.     

一般无约束优化问题的广义拟牛顿法

对一般目标函数极小化问题的拟牛顿法及其全局收敛性的研究,已经成为拟牛顿法理论中最基本的开问题之一．本文对这个问题做了进一步的研究,对无约束优化问题提出一类新的广义拟牛顿算法,并结合Goldstein线搜索证明了算法对一般非凸目标函数极小化问题的全局收敛性．     

一种无约束全局优化的水平值下降算法

本文研究无约束全局优化问题,建立了一种新的水平值下降算法(Level-value Descent Method,LDM).讨论并建立了概率意义下取全局最小值的一个充分必要条件,证明了算法LDM是依概率测度收敛的.这种LDM算法是基于重点度取样(Improtance Sampling)和Markov链Monte-Carlo随机模拟实现的,并利用相对熵方法(TheCross-Entropy Method)自动更新取样密度,算例表明LDM算法具有较高的数值精度和较好的全局收敛性.     

Stochastic Method for the Solution of Unconstrained Vector Optimization Problems

We propose a new stochastic algorithm for the solution of unconstrained vector optimization problems, which is based on a special class of stochastic differential equations. An efficient algorithm for the numerical solution of the stochastic differential equation is developed. Interesting properties of the algorithm enable the treatment of problems with a large number of variables. Numerical results are given.