共查询到19条相似文献,搜索用时 941 毫秒
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一个新的无约束优化超记忆梯度算法 总被引:3,自引:0,他引:3
本文提出一种新的无约束优化超记忆梯度算法,算法利用当前点的负梯度和前一点的负梯度的线性组合为搜索方向,以精确线性搜索和Armijo搜索确定步长.在很弱的条件下证明了算法具有全局收敛性和线性收敛速度.因算法中避免了存贮和计算与目标函数相关的矩阵,故适于求解大型无约束优化问题.数值实验表明算法比一般的共轭梯度算法有效. 相似文献
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大步长非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法的全局收敛性 总被引:3,自引:0,他引:3
本文在ZhangH.C.的非单调线搜索规则基础上,结合ShiZ.J.大步长线搜索技巧提出了新的大步长的非单调线搜索规则,设计了求解无约束最优化问题的大步长非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法,在△f(x)一致连续的条件下给出了算法的全局收敛性和超线性收敛性分析.数值例子表明算法是有效的,适合求解大规模问题. 相似文献
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一类非单调算法的收敛性质 总被引:1,自引:0,他引:1
1.搜索步长和搜索方向对于无约束最优化问题(?)f(x),其中f:R~n→R~1,f∈C~1,一般采用形如x_(k 1)=x_k λ_kd_k(k=1,2,…)的迭代算法来求解,这里λ_k为搜索步长,d_k为搜索方向. 相似文献
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一类非单调算法的收敛性质 总被引:2,自引:0,他引:2
1.搜索步长和搜索方向对于无约束最优化问题(?)f(x),其中f:R~n→R~1,f∈C~1,一般采用形如x_(k+1)=x_k+λ_kd_k(k=1,2,…)的迭代算法来求解,这里λ_k为搜索步长,d_k为搜索方向. 相似文献
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提出一类新的求解无约束优化问题的记忆梯度法,在较弱条件下证明了算法具有全局收敛性和线性收敛速率.算法采用曲线搜索方法,在每一步同时确定搜索方向和步长,收敛稳定,并且不需计算和存储矩阵,适于求解大规模优化问题.数值试验表明算法是有效的. 相似文献
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广义拟牛顿算法对一般目标函数的收敛性 总被引:2,自引:0,他引:2
本文证明了求解无约束最优化的广义拟牛顿算法在Goldstein非精确线搜索下对一般目标函数的全局收敛性,并在一定条件下证明了算法的局部超线性收敛性。 相似文献
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In this paper acceptability criteria for the linesearch stepsize are introduced which require only function values. Simple
algorithm models based on these criteria are presented. Some modifications of criteria based on the knowledge of the directional
derivative are also illustrated.
This paper was written while this author was visiting CRAI. 相似文献
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关于外梯度法的步长规则 总被引:1,自引:0,他引:1
1.引言 设为Rn中的一个非空闭凸集,F(x)为Rn Rn中的一个连续向量函数.变分不等式问题(F,)就是:找一向量x 使得当 =R时,(1.1)退化成非线性互补问题。在这篇文章中总假定:(H1) ,这里表示(1.1)的解集;(H2)F(x)是单调的,即对,(x-y)(F(x)-F(x)-F(y)). 这类问题出现在工程物理、经济管理等领域,有着极为广泛的应用.因此,其数值解近年来受到重视,提出许多有效算法,见综述[1, 2].在现有的算法中, Korpelevich的外梯度法[3](何炳生称它为投影… 相似文献
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Conditions on Runge-Kutta algorithms can be obtained which ensuresmooth stepsize selection when stability of the algorithm isrestricting the stepsize. Some recently derived results areshown to hold for a more general test problem. 相似文献
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《Applied Mathematics Letters》2002,15(2):181-185
In this paper, we propose a new stepsize rule in He and Zhou's alternating direction method. Under this new stepsize strategy, we extend their method for solving convex quadratic minimization problems to also monotone linear variational inequality problems. 相似文献
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考虑约束最优化问题:minx∈Ωf(x)其中:f:R^n→R是连续可微函数,Ω是一闭凸集。本文研究了解决此问题的梯度投影方法,在步长的选取时采用了一种新的策略,在较弱的条件下,证明了梯度投影响方法的全局收敛性。 相似文献
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Yunmei Chen William W. Hager Maryam Yashtini Xiaojing Ye Hongchao Zhang 《Computational Optimization and Applications》2013,54(2):317-342
This paper develops a Bregman operator splitting algorithm with variable stepsize (BOSVS) for solving problems of the form $\min\{\phi(Bu) +1/2\|Au-f\|_{2}^{2}\}$ , where ? may be nonsmooth. The original Bregman Operator Splitting (BOS) algorithm employed a fixed stepsize, while BOSVS uses a line search to achieve better efficiency. These schemes are applicable to total variation (TV)-based image reconstruction. The stepsize rule starts with a Barzilai-Borwein (BB) step, and increases the nominal step until a termination condition is satisfied. The stepsize rule is related to the scheme used in SpaRSA (Sparse Reconstruction by Separable Approximation). Global convergence of the proposed BOSVS algorithm to a solution of the optimization problem is established. BOSVS is compared with other operator splitting schemes using partially parallel magnetic resonance image reconstruction problems. The experimental results indicate that the proposed BOSVS algorithm is more efficient than the BOS algorithm and another split Bregman Barzilai-Borwein algorithm known as SBB. 相似文献
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We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based
technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions:
the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative curvature direction.
A test based on the quadratic model of the objective function is used to select the most promising between the two search
directions. Both the latter selection rule and the CG stopping criterion for approximately solving Newton’s equation, strongly
rely on conjugacy conditions. An appropriate linesearch technique is adopted for each search direction: a nonmonotone stabilization
is used with the approximate Newton step, while an Armijo type linesearch is used for the negative curvature direction. The
proposed algorithm is both globally and superlinearly convergent to stationary points satisfying second order necessary conditions.
We carry out a significant numerical experience in order to test our proposal. 相似文献