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本文针对大规模无约束优化问题研究了一个新的有限内存信赖域实现方法,提出了一个在有限维(维数≤2m+1)子空间上精确求解信赖域子问题的方法,大大减少了计算量;分析了方法的收敛性,并详细给出了数值计算方法,最后通过数值实验验证了方法的有效性. 相似文献
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Yuhong Dai Dachuan Xu 《计算数学(英文版)》2003,(2)
Trust region (TR) algorithms are a class of recently developed algorithms for nonlinear optimization. A new family of TR algorithms for unconstrained optimization, which is the extension of the usual TR method, is presented in this paper. When the objective function is bounded below and continuously, differentiable, and the norm of the Hesse approximations increases at most linearly with the iteration number, we prove the global convergence of the algorithms. Limited numerical results are reported, which indicate that our new TR algorithm is competitive. 相似文献
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Jinghui Liu Changfeng Ma 《计算数学(英文版)》2014,(4):476-490
Based on the nonmonotone line search technique proposed by Gu and Mo (Appl. Math. Comput. 55, (2008) pp. 2158-2172), a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio ρk for evaluating the trial step dk whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems. 相似文献
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CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION 总被引:11,自引:0,他引:11
De-tong Zhu 《计算数学(英文版)》2001,19(3):241-258
1. Illtroductioncrust region method is a well-accepted technique in nonlinear optindzation to assure globalconvergence. One of the adVantages of the model is that it does not require the objectivefunction to be convex. Many differellt versions have been suggested in using trust regiontechnique. For each iteration, suppose a current iterate point, a local quadratic model of thefunction and a trust region with center at the point and a certain radius are given. A point thatminimizes the model f… 相似文献
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Wen-yuSun Jin-yunYuan Ya-xiangYuan 《计算数学(英文版)》2003,21(3):295-304
In this paper we present a trust region method of conic model for linearly constrained optimization problems.We discuss trust region approaches with conic model subproblems.Some equivalent variation properties and optimality conditions are given.A trust region algorithm based on conic model is constructed.Global convergence of the method is established. 相似文献
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梯度法是求解无约束最优化的一类重要方法.步长选取的好坏与梯度法的数值表现息息相关.注意到BB步长隐含了目标函数的二阶信息,本文将BB法与信赖域方法相结合,利用BB步长的倒数去近似目标函数的Hesse矩阵,同时利用信赖域子问题更加灵活地选取梯度法的步长,给出求解无约束最优化问题的单调和非单调信赖域BB法.在适当的假设条件下,证明了算法的全局收敛性.数值试验表明,与已有的求解无约束优化问题的BB类型的方法相比,非单调信赖域BB法中e_k=‖x_k-x~*‖的下降呈现更明显的阶梯状和单调性,因此收敛速度更快. 相似文献
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一个解无约束优化问题的过滤信赖域方法 总被引:4,自引:0,他引:4
1 引言 本文中,我们考虑一般的无约束极小化问题: minx∈Rn f(x), (1.1) 其中f:Rn→R二次连续可微. 信赖域方法是解问题(1.1)的一类非常成功的算法.在标准信赖域算法框架([2][11][1])中,迭代点列是单调下降的,对于一些坏条件问题,会出现收敛非常缓慢的情形.针对这种问题,人们提出了非单调技术([2][3][13][14][15]),来加快算法在实际计算中的收敛速度,取得了很好的数值效果. 相似文献
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本文研究求解含有奇异解的无约束最优化问题算法 .该类问题的一个重要特性是目标函数的Hessian阵可能处处奇异 .我们提出求解该类问题的一种梯度 -正则化牛顿型混合算法 .并在一定的条件下得到了算法的全局收敛性 .而且 ,经一定迭代步后 ,算法还原为正则化 Newton法 .因而 ,算法具有局部二次收敛性 . 相似文献
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求解变量带简单界约束的非线性规划问题的信赖域方法 总被引:3,自引:0,他引:3
1.引言。本文考虑下述变量带简单界约束的非线性规划问题:问题(1.1)不仅是实际应用中出现的简单的约束最优化问题,而且相当一部分最优化问题可以把变量限制在有意义的区间内181.因此,无论在理论方面还是在实际应用方面,都有必要研究此种问题.给出简便而且有效的算法.有些文章提出了一些特殊的方法.如011和[2].14]及16]提出了一类信赖域方法,它们都借助于某种辅助点,证明了算法的全局收敛性.在收敛速度的分析方面,除要求在*-T点满足严格互补松弛外,它们还要求另一个条件,即在每次迭代中,辅助点的有效约束必须在尝… 相似文献
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§1 IntroductionIn this paper we analyze an interior point scaling projected reduced Hessian methodwith trust region strategy for solving the nonlinear equality constrained optimizationproblem with nonnegative constraints on variables:min f(x)s.t. c(x) =0 (1.1)x≥0where f∶Rn→R is the smooth nonlinear function,notnecessarily convex and c(x)∶Rn→Rm(m≤n) is the vector nonlinear function.There are quite a few articles proposing localsequential quadratic programming reduced Hessian methods… 相似文献
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无约束非光滑优化问题的信赖域算法及收敛性 总被引:9,自引:0,他引:9
1.引言考虑下列无约束非光滑优化问题:其中f为R”上的局部LIPSChitZ函数.本文将11·112简记为11·l.信赖域算法是通过求解一系列子问题3*B(二,凸):来求解问题(1)的,其中拉x,·)为j在x点的一阶近似,B为nxn阶对称阵.下面给出信赖域的基本算法TRA:步1·给定... 相似文献
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<正>1引言本文考虑求解大规模无约束最优化问题■f(x):(1.1)其中f:R~n→R是二阶连续可微的实值目标函数,n是一个比较大的正整数.在求解问题(1.1)时,通常的迭代法产生一个迭代点列x_0,x_1,x_2,…,其中x_(k+1)由x_k产生.在每一步迭代中,算法首先解一个信赖域子问题:■m_k(s)■g_k~T s+1/2s~TH_ks,s.t.||s||≤△_k,(1.2) 相似文献
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本文研究了约束优化信赖域法中的线性化约束条件在信赖域内无解的问题.利用一种基于增广Lagrange函数的方法.获得了一个改进的约束优化的信赖域法.该法的线性化约束条件在信赖内有解,并且具有全局收敛性和超线性收敛性. 相似文献
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§ 1 IntroductionIn this paper we consider the following unconstrained optimization problem:minx∈ Rnf( x) , ( 1 )where f:Rn→R is a convex LC1 function,i.e.,a continuously differentiable convex func-tion whose gradient is Lipschitz continuous.We call the problem( 1 ) a convex LC1 opti-mization problem.This problem is an importantsubjectin nonlinear optimization.Applica-tions of such a minimization problem include stochastic quadratic programs[1 ,2 ] and the ex-tended linear-quadratic pro… 相似文献
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非线性不等式约束最优化快速收敛的可行信赖域算法 总被引:5,自引:0,他引:5
In this paper,by combining the trust region technique with the generalized gradient projection.a new trust region algorithm with feasible iteration points is presented for nonlinear inequality constrained optimization,and its trust region is a general compact set containing the origion as an inteior point.No penalty function is used in the algorithm,and it is feasible descent .Under suitable assumptions,the algorithm is proved to possess global and strong convergence as well as superlinear and quadratic convergence.Some numerical results are reported. 相似文献
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一种求解无约束极值问题的无记忆拟牛顿算法 总被引:5,自引:0,他引:5
§1.引言 求无约束极值常用的方法,有CG算法、变尺度算法以及拟牛顿算法等等.变尺度算法虽然收敛速度快,但是存贮量大(为O(n~2))。CG算法所需存贮量(为O(n))虽小,但在收敛速度上一般不如变尺度法.因此,本文探索收敛速度快且所需存贮量小的算法,以 相似文献
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