一个新的MBFGS信赖域算法

本文研究了无约束最优化问题.利用MBFGS信赖域算法的基本思想,通过对BFGS校正公式的改进,并结合线搜索技术,提出了一种新的MBFGS信赖域算法,拓宽了信赖域算法的适用范围,并在一定条件下证明了该算法的全局收敛性和超线性收敛性.     

求解一般约束优化问题的修正BFGS信赖域算法

借鉴无约束优化问题的BFGS信赖域算法,建立了非线性一般约束优化问题的BFGS信赖域算法,并证明了算法的全局收敛性．数值实验表明,算法是有效的．     

一个带有线搜索的新信赖域方法及其收敛性

本文利用一个修正的BFGS公式,提出了一个结合Armijo线搜索条件技术的BFGS信赖域方法,并在一定条件下证明了该方法的全局收敛性和超线性收敛性.初步的数值实验结果表明该方法是有效的.     

解无约束优化问题的一个新的带线搜索的信赖域算法

在传统信赖域方法的基础上, 提出了求解无约束最优化问题的一个新的带线搜索的信赖域算法. 该算法采用大步长 Armijo 线搜索技术获得迭代步长, 克服了每次迭代求解信赖域子问题时计算量较大的缺点, 因而适用于求解大型的优化问题. 在适当的条件下, 我们证明了算法的全局收敛性. 数值实验结果表明本文所提出的算法是有效的.     

非线性最小二乘问题的信赖域方法

本文提出一个新的非线性最小二乘的信赖域方法,在该方法中每个信赖域子问题只需要一次求解,而且每次迭代的一维搜索步长因子是给定的,避开一维搜索的环节,大大地提高了算法效率.文中证明了在一定的条件下算法的全局收敛性.     

面向全局优化基于分形的混合混沌优化算法

Julia集具有分形结构,一旦确定吸引域边界上任一点,就可通向任一个吸引周期点的吸引域.Newton-Raphson法利用此性质可计算方程所有根,并可精确计算BFGS法和共轭梯度法中下降方向步长,将两种算法分别与混沌优化算法结合,因而从新的视角建立一种融合分形理论的混合混沌优化算法.研究表明,所提出算法的计算效率高于利用Wolf一维不精确搜索求得步长的混合算法,而且混合混沌BFGS算法的优化能力优于混合混沌共轭梯度算法,也说明BFGS的局部搜索能力比共轭梯度法强.     

一个锥模型的自适应信赖域算法及其收敛性

本文研究了无约束最优化问题的基于锥模型的自适应信赖域算法.利用理论分析得到一个新的自适应信赖域半径.算法在每步迭代中以变化的速率、当前迭代点的信息以及水平向量信息调节信赖域半径的大小.从理论上证明了新算法的全局收敛性和Q-二阶收敛性.用数值试验验证了新算法的有效性.推广了已有的自适应信赖域算法的可行性和有效性.     

一类新拟牛顿非单调信赖域算法

提出了一类新的求解无约束最优化问题的新拟牛顿非单调信赖域算法.采用加权的r_k用以调整信赖域半径,在适当的条件下,证明了算法的全局收敛性.数值结果表明算法的有效性.     

结合有效集和多维滤子技术的拟Newton信赖域算法(英文)

针对界约束优化问题,提出一个修正的多维滤子信赖域算法.将滤子技术引入到拟Newton信赖域方法,在每步迭代,Cauchy点用于预测有效集,此时试探步借助于求解一个较小规模的信赖域子问题获得.在一定条件下,本文所提出的修正算法对于凸约束优化问题全局收敛.数值试验验证了新算法的实际运行结果.     

一类带线搜索的非单调信赖域新算法

结合非单调信赖域方法,和非单调线搜索技术,提出了一种新的无约束优化算法.信赖域方法的每一步采用线搜索,使得迭代每一步都充分下降加快了迭代速度.在一定条件下,证明了算法具有全局收敛性和局部超线性.收敛速度.数值试验表明算法是十分有效的.     

An effective adaptive trust region algorithm for nonsmooth minimization

In this paper, an adaptive trust region algorithm that uses Moreau–Yosida regularization is proposed for solving nonsmooth unconstrained optimization problems. The proposed algorithm combines a modified secant equation with the BFGS update formula and an adaptive trust region radius, and the new trust region radius utilizes not only the function information but also the gradient information. The global convergence and the local superlinear convergence of the proposed algorithm are proven under suitable conditions. Finally, the preliminary results from comparing the proposed algorithm with some existing algorithms using numerical experiments reveal that the proposed algorithm is quite promising for solving nonsmooth unconstrained optimization problems.     

A new adaptive trust region algorithm for optimization problems

It is well known that trust region methods are very effective for optimization problems. In this article, a new adaptive trust region method is presented for solving unconstrained optimization problems. The proposed method combines a modified secant equation with the BFGS updated formula and an adaptive trust region radius, where the new trust region radius makes use of not only the function information but also the gradient information. Under suitable conditions, global convergence is proved, and we demonstrate the local superlinear convergence of the proposed method. The numerical results indicate that the proposed method is very efficient.     

一个等式约束问题的拟Newton—信赖域型方法及其收敛性

在[1]中,Vardi提出一个信赖域方法,而收敛性证明却是在精确λ-搜索下给出的,本文在[1]的基础上提出一个新的算法-拟Newton-信赖域型算法,并证明该算法是全局收敛的,通过利用二阶修正技术去修正该算法,我们证明了该算法是局部超线性收敛的。     

A NONMONOTONE TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION SUBJECT TO GENERAL CONSTRAINTS

In this paper we present a nonmonotone trust region algorithm for general nonlinear constrained optimization problems. The main idea of this paper is to combine Yuan's technique[1] with a nonmonotone method similar to Ke and Han [2]. This new algorithm may not only keep the robust properties of the algorithm given by Yuan, but also have some advantages led by the nonmonotone technique. Under very mild conditions, global convergence for the algorithm is given. Numerical experiments demonstrate the efficiency of the algorithm.     

A Nonmonotone Trust Region Algorithm for Nonlinear Optimization Subject to General Constraints

In this paperwe present a nonmonotone trust region algorthm for general nonlinear constrained optimization problems.The main idea of this paper is to combine Yuan‘‘‘‘s technique[1]with a nonmonotone method similar to Ke and Han[2].This new algorithm may not only keep the robust properties of the algorithm given by Yuan,but also have some advantages led by the nonmonotone technique.Under very mild conditions,global convergence for the algorithm is given.Numerical experiments demostrate the efficency of the algorithm.     

A modified SLP algorithm and its global convergence

This paper concerns a filter technique and its application to the trust region method for nonlinear programming (NLP) problems. We used our filter trust region algorithm to solve NLP problems with equality and inequality constraints, instead of solving NLP problems with just inequality constraints, as was introduced by Fletcher et al. [R. Fletcher, S. Leyffer, Ph.L. Toint, On the global converge of an SLP-filter algorithm, Report NA/183, Department of Mathematics, Dundee University, Dundee, Scotland, 1999]. We incorporate this filter technique into the traditional trust region method such that the new algorithm possesses nonmonotonicity. Unlike the tradition trust region method, our algorithm performs a nonmonotone filter technique to find a new iteration point if a trial step is not accepted. Under mild conditions, we prove that the algorithm is globally convergent.     

A scaled BFGS preconditioned conjugate gradient algorithm for unconstrained optimization

This letter presents a scaled memoryless BFGS preconditioned conjugate gradient algorithm for solving unconstrained optimization problems. The basic idea is to combine the scaled memoryless BFGS method and the preconditioning technique in the frame of the conjugate gradient method. The preconditioner, which is also a scaled memoryless BFGS matrix, is reset when the Powell restart criterion holds. The parameter scaling the gradient is selected as the spectral gradient. Computational results for a set consisting of 750 test unconstrained optimization problems show that this new scaled conjugate gradient algorithm substantially outperforms known conjugate gradient methods such as the spectral conjugate gradient SCG of Birgin and Martínez [E. Birgin, J.M. Martínez, A spectral conjugate gradient method for unconstrained optimization, Appl. Math. Optim. 43 (2001) 117–128] and the (classical) conjugate gradient of Polak and Ribière [E. Polak, G. Ribière, Note sur la convergence de méthodes de directions conjuguées, Revue Francaise Informat. Reserche Opérationnelle, 3e Année 16 (1969) 35–43], but subject to the CPU time metric it is outperformed by L-BFGS [D. Liu, J. Nocedal, On the limited memory BFGS method for large scale optimization, Math. Program. B 45 (1989) 503–528; J. Nocedal. http://www.ece.northwestern.edu/~nocedal/lbfgs.html].