共查询到19条相似文献,搜索用时 128 毫秒
1.
本文提供修正近似信赖域类型路经三类预条件弧线路径方法解无约束最优化问题.使用对称矩阵的稳定Bunch-Parlett易于形成信赖域子问题的弧线路径,使用单位下三角矩阵作为最优路径和修正梯度路径的预条件因子.运用预条件因子改进Hessian矩阵特征值分布加速预条件共轭梯度路径收敛速度.基于沿着三类路径信赖域子问题产生试探步,将信赖域策略与非单调线搜索技术相结合作为新的回代步.理论分析证明在合理条件下所提供的算法是整体收敛性,并且具有局部超线性收敛速率,数值结果表明算法的有效性. 相似文献
2.
提出非线性等式和有界约束优化问题的结合非单调技术的仿射信赖域方法.
结合信赖域方法和内点回代线搜索技术, 每一步迭代转到由一般信赖域子问题产生的回代步中且满足严格内点可行条件.
在合理的假设条件下, 证明了算法的整体收敛性和局部超线性收敛速率.
最后, 数值结果表明了所提供的算法具有有效性. 相似文献
3.
投影信赖域策略结合非单调线搜索算法解有界约束非线性半光滑方程组.基于简单有界约束的非线性优化问题构建信赖域子问题,半光滑类牛顿步在可行域投影得到投影牛顿的试探步,获得新的搜索方向,结合非单调线搜索技术得到回代步,获得新的步长.在合理的条件下,证明算法不仅具有整体收敛性且保持超线性收敛速率.引入非单调技术能克服高度非线性的病态问题,加速收敛性进程,得到超线性收敛速率. 相似文献
4.
提供了一种新的非单调内点回代线搜索技术的仿射内点信赖域方法解线性不等式约束的广义非线性互补问题(GCP).基于广义互补问题构成的半光滑方程组的广义Jacobian矩阵,算法使用l_2范数作为半光滑方程组的势函数,形成的信赖域子问题为一个带椭球约束的线性化的二次模型.利用广义牛顿方程计算试探迭代步,通过内点映射回代技术确保迭代点是严格内点,保证了算法的整体收敛性.在合理的条件下,证明了信赖域算法在接近最优点时可转化为广义拟牛顿步,进而具有局部超线性收敛速率.非单调技术将克服高度非线性情况加速收敛进展.最后,数值结果表明了算法的有效性. 相似文献
5.
提供了一种新的非单调内点回代线搜索技术的仿射内点信赖域方法解线性不等式约束的广义非线性互补问题(GCP).基于广义互补问题构成的半光滑方程组的广义Jacobian矩阵,算法使用l2范数作为半光滑方程组的势函数,形成的信赖域子问题为一个带椭球约束的线性化的二次模型.利用广义牛顿方程计算试探迭代步,通过内点映射回代技术确保迭代点是严格内点,保证了算法的整体收敛性.在合理的条件下,证明了信赖域算法在接近最优点时可转化为广义拟牛顿步,进而具有局部超线性收敛速率.非单调技术将克服高度非线性情况加速收敛进展.最后,数值结果表明了算法的有效性. 相似文献
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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. 相似文献
8.
本文结合非单调内点回代技术,提供了新的仿射信赖域方法解含有非负变量约束和非线性等式约束的优化问题.为求解大规模问题,采用等式约束的Jacobian矩阵的QR分解和两块校正的双边既约Hessian矩阵投影,将问题分解成零空间和值空间两个信赖域子问题.零空间的子问题为通常二次目标函数只带椭球约束的信赖域子问题,而值空间的子问题使用满足信赖域约束参数的值空间投影向量方向.通过引入Fletcher罚函数作为势函数,将由两个子问题结合信赖域策略构成的合成方向,并使用非单调线搜索技术回代于可接受的非负约束内点步长.在合理的条件下,算法具有整体收敛性且两块校正的双边既约Hessian投影法将保持超线性收敛速率.非单调技术将克服高度非线性情况,加快收敛进展. 相似文献
9.
朱德通 《数学年刊A辑(中文版)》2005,(4)
本文结合非单调内点回代技术,提供了新的仿射信赖域方法解含有非负变量约束和非线性等式约束的优化问题.为求解大规模问题,采用等式约束的Jacobian矩阵的QR分解和两块校正的双边既约Hessian矩阵投影,将问题分解成零空间和值空间两个信赖域子问题.零空间的子问题为通常二次目标函数只带椭球约束的信赖域子问题,而值空间的子问题使用满足信赖域约束参数的值空间投影向量方向.通过引入Fletcher罚函数作为势函数,将由两个子问题结合信赖域策略构成的合成方向,并使用非单调线搜索技术回代于可接受的非负约束内点步长.在合理的条件下,算法具有整体收敛性且两块校正的双边既约Hessian投影法将保持超线性收敛速率.非单调技术将克服高度非线性情况,加快收敛进展. 相似文献
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11.
§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
12.
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
13.
朱德通 《高校应用数学学报(英文版)》2004,19(3):311-326
A interior point scaling projected reduced Hessian method with combination of nonmonotonic backtracking technique and trust region strategy for nonlinear equality constrained optimization with nonegative constraint on variables is proposed. In order to deal with large problems,a pair of trust region subproblems in horizontal and vertical subspaces is used to replace the general full trust region subproblem. The horizontal trust region subproblem in the algorithm is only a general trust region subproblem while the vertical trust region subproblem is defined by a parameter size of the vertical direction subject only to an ellipsoidal constraint. Both trust region strategy and line search technique at each iteration switch to obtaining a backtracking step generated by the two trust region subproblems. By adopting the l1 penalty function as the merit function, the global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion and the second order correction step are used to overcome Maratos effect and speed up the convergence progress in some ill-conditioned cases. 相似文献
14.
《Journal of Computational and Applied Mathematics》2005,173(1):115-148
In this paper, we propose a new nonmonotonic interior point backtracking strategy to modify the reduced projective affine scaling trust region algorithm for solving optimization subject to nonlinear equality and linear inequality constraints. The general full trust region subproblem for solving the nonlinear equality and linear inequality constrained optimization is decomposed to a pair of trust region subproblems in horizontal and vertical subspaces of linearize equality constraints and extended affine scaling equality constraints. The horizontal subproblem in the proposed algorithm is defined by minimizing a quadratic projective reduced Hessian function subject only to an ellipsoidal trust region constraint in a null subspace of the tangential space, while the vertical subproblem is also defined by the least squares subproblem subject only to an ellipsoidal trust region constraint. By introducing the Fletcher's penalty function as the merit function, trust region strategy with interior point backtracking technique will switch to strictly feasible interior point step generated by a component direction of the two trust region subproblems. The global convergence of the proposed algorithm while maintaining fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some high nonlinear function conditioned cases. 相似文献
15.
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. 相似文献
16.
A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints 总被引:12,自引:0,他引:12
A trust region and affine scaling interior point method (TRAM) is proposed for a general nonlinear minimization with linear
inequality constraints [8]. In the proposed approach, a Newton step is derived from the complementarity conditions. Based
on this Newton step, a trust region subproblem is formed, and the original objective function is monotonically decreased.
Explicit sufficient decrease conditions are proposed for satisfying the first order and second order necessary conditions.?The
objective of this paper is to establish global and local convergence properties of the proposed trust region and affine scaling
interior point method. It is shown that the proposed explicit decrease conditions are sufficient for satisfy complementarity,
dual feasibility and second order necessary conditions respectively. It is also established that a trust region solution is
asymptotically in the interior of the proposed trust region subproblem and a properly damped trust region step can achieve
quadratic convergence.
Received: January 29, 1999 / Accepted: November 22, 1999?Published online February 23, 2000 相似文献
17.
Qun-yan Zhou Wen-yu Sun 《计算数学(英文版)》2006,24(6):761-770
In this paper,an algorithm for unconstrained optimization that employs both trustregion techniques and curvilinear searches is proposed.At every iteration,we solve thetrust region subproblem whose radius is generated adaptively only once.Nonmonotonicbacktracking curvilinear searches are performed when the solution of the subproblem isunacceptable.The global convergence and fast local convergence rate of the proposedalgorithms are established under some reasonable conditions.The results of numericalexperiments are reported to show the effectiveness of the proposed algorithms. 相似文献
18.
A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS:Ⅰ. ALGORITHM AND GLOBAL CONVERGENCE 总被引:1,自引:1,他引:0
XIUNAIHUA 《高校应用数学学报(英文版)》1995,10(3):287-296
A class of trust region methods tor solving linear inequality constrained problems is propo6ed in this paper. It is shown that the algorithm is of global convergence. The algorithm uses a version of the two-slded projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm. 相似文献
19.
(Institute of Applied Mathematics Academia Sinica Beijing ).(Current address: Department of Mathematics Hebei Teacher's College Shijiazhuang ). 《高校应用数学学报(英文版)》1995,(3)
ACLASSOFTRUSTREGIONMETHODSFORLINEARINEQUALITYCONSTRAINEDOPTIMIZATIONANDITSTHEORYANALYSIS:I.ALGORITHMANDGLOBALCONVERGENCEXIUNA... 相似文献