共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, a new type of stepsize, approximate optimal stepsize, for gradient method is introduced to interpret the Barzilai–Borwein (BB) method, and an efficient gradient method with an approximate optimal stepsize for the strictly convex quadratic minimization problem is presented. Based on a multi-step quasi-Newton condition, we construct a new quadratic approximation model to generate an approximate optimal stepsize. We then use the two well-known BB stepsizes to truncate it for improving numerical effects and treat the resulted approximate optimal stepsize as the new stepsize for gradient method. We establish the global convergence and R-linear convergence of the proposed method. Numerical results show that the proposed method outperforms some well-known gradient methods. 相似文献
2.
B. S. He H. Yang Q. Meng D. R. Han 《Journal of Optimization Theory and Applications》2002,112(1):129-143
In this paper, we present a modified Goldstein–Levitin–Polyak projection method for asymmetric strongly monotone variational inequality problems. A practical and robust stepsize choice strategy, termed self-adaptive procedure, is developed. The global convergence of the resulting algorithm is established under the same conditions used in the original projection method. Numerical results and comparison with some existing projection-type methods are given to illustrate the efficiency of the proposed method. 相似文献
3.
一类新的非单调记忆梯度法及其全局收敛性 总被引:1,自引:0,他引:1
在非单调Armijo线搜索的基础上提出一种新的非单调线搜索,研究了一类在该线搜索下的记忆梯度法,在较弱条件下证明了其全局收敛性。与非单调Armijo线搜索相比,新的非单调线搜索在每次迭代时可以产生更大的步长,从而使目标函数值充分下降,降低算法的计算量。 相似文献
4.
无约束最优化线搜索一般模型及BFGS方法的整体收敛性 总被引:7,自引:0,他引:7
本文给出了无约束最优化的算法中线性搜索的可接受的步长选择律的一种一般形式,它概括了大多数已有的步长律为其特例,并且研究了它基本性质,最后证明了此线性搜索一般模拟相结合的无约束优化的BFGS算法的整体收敛性。 相似文献
5.
In this paper, we suggest and analyze a new self-adaptive inexact implicit method with a variable parameter for general mixed
quasi variational inequalities, where the skew-symmetry of the nonlinear bifunction plays a crucial part in the convergence
analysis of this method. We use a self-adaptive technique to adjust parameter ρ at each iteration. The global convergence of the proposed method is proved under some mild conditions. Preliminary numerical
results indicate that the self-adaptive adjustment rule is necessary in practice.
Muhammad Aslam Noor is supported by the Higher Education Commission, Pakistan, through research grant No: 1-28/HEC/HRD/2005/90. 相似文献
6.
In this paper we present several relaxed inexact projection methods for the split feasibility problem (SFP). Each iteration of the first proposed algorithm consists of a projection onto a halfspace containing the given closed convex set. The algorithm can be implemented easily and its global convergence to the solution can be established under suitable conditions. Moreover,we present some modifications of the relaxed inexact projection method with constant stepsize by adopting Armijo-like search. We furthermore present a variable-step relaxed inexact projection method which does not require the computation of the matrix inverses and the largest eigenvalue of the matrix ATA, and the objective function can decrease sufficiently at each iteration. We show convergence of these modified algorithms under mild conditions. Finally, we perform some numerical experiments, which show the behavior of the algorithms proposed. 相似文献
7.
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
8.
We propose a new inexact line search rule and analyze the global convergence and convergence rate of related descent methods.
The new line search rule is similar to the Armijo line-search rule and contains it as a special case. We can choose a larger
stepsize in each line-search procedure and maintain the global convergence of related line-search methods. This idea can make
us design new line-search methods in some wider sense. In some special cases, the new descent method can reduce to the Barzilai
and Borewein method. Numerical results show that the new line-search methods are efficient for solving unconstrained optimization
problems.
The work was supported by NSF of China Grant 10171054, Postdoctoral Fund of China, and K. C. Wong Postdoctoral Fund of CAS
Grant 6765700.
The authors thank the anonymous referees for constructive comments and suggestions that greatly improved the paper. 相似文献
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10.
In this work we analyze a first order method especially tailored for smooth saddle point problems, based on an alternating extragradient scheme. The proposed method is based on three successive projection steps, which can be computed also with respect to non Euclidean metrics. The stepsize parameter can be adaptively computed, so that the method can be considered as a black-box algorithm for general smooth saddle point problems. We develop the global convergence analysis in the framework of non Euclidean proximal distance functions, under mild local Lipschitz conditions, proving also the \(\mathcal {O}(\frac{1}{k})\) rate of convergence on the primal–dual gap. Finally, we analyze the practical behavior of the method and its effectiveness on some applications arising from different fields. 相似文献
11.
Dang Van Hieu Yeol Je Cho Yi‐Bin Xiao 《Mathematical Methods in the Applied Sciences》2019,42(18):6067-6082
In this paper, we introduce two golden ratio algorithms with new stepsize rules for solving pseudomonotone and Lipschitz variational inequalities in finite dimensional Hilbert spaces. The presented stepsize rules allow the resulting algorithms to work without the prior knowledge of the Lipschitz constant of operator. The first algorithm uses a sequence of stepsizes that is previously chosen, diminishing, and nonsummable, while the stepsizes in the second one are updated at each iteration and by a simple computation. A special point is that the sequence of stepsizes generated by the second algorithm is separated from zero. The convergence and the convergence rate of the proposed algorithms are established under some standard conditions. Also, we give several numerical results to show the behavior of the algorithms in comparison with other algorithms. 相似文献
12.
H. Mukai 《Mathematical Programming》1979,17(1):298-319
Conjugate gradient methods have been extensively used to locate unconstrained minimum points of real-valued functions. At present, there are several readily implementable conjugate gradient algorithms that do not require exact line search and yet are shown to be superlinearly convergent. However, these existing algorithms usually require several trials to find an acceptable stepsize at each iteration, and their inexact line search can be very timeconsuming.In this paper we present new readily implementable conjugate gradient algorithms that will eventually require only one trial stepsize to find an acceptable stepsize at each iteration.Making usual continuity assumptions on the function being minimized, we have established the following properties of the proposed algorithms. Without any convexity assumptions on the function being minimized, the algorithms are globally convergent in the sense that every accumulation point of the generated sequences is a stationary point. Furthermore, when the generated sequences converge to local minimum points satisfying second-order sufficient conditions for optimality, the algorithms eventually demand only one trial stepsize at each iteration, and their rate of convergence isn-step superlinear andn-step quadratic.This research was supported in part by the National Science Foundation under Grant No. ENG 76-09913. 相似文献
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14.
In this paper, a new nonmonotone inexact line search rule is proposed and applied to the trust region method for unconstrained optimization problems. In our line search rule, the current nonmonotone term is a convex combination of the previous nonmonotone term and the current objective function value, instead of the current objective function value . We can obtain a larger stepsize in each line search procedure and possess nonmonotonicity when incorporating the nonmonotone term into the trust region method. Unlike the traditional trust region method, the algorithm avoids resolving the subproblem if a trial step is not accepted. Under suitable conditions, global convergence is established. Numerical results show that the new method is effective for solving unconstrained optimization problems. 相似文献
15.
In this paper, we present a new memory gradient method such that the direction generated by this method provides a sufficient descent direction for the objective function at every iteration. Then, we analyze its global convergence under mild conditions and convergence rate for uniformly convex functions. Finally, we report some numerical results to show the efficiency of the proposed method. 相似文献
16.
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
17.
In this paper, we introduce a new concept of approximate optimal stepsize for gradient method, use it to interpret the Barzilai-Borwein (BB) method, and present an efficient gradient method with approximate optimal stepsize for large unconstrained optimization. If the objective function f is not close to a quadratic on a line segment between the current iterate x k and the latest iterate x k?1, we construct a conic model to generate the approximate optimal stepsize for gradient method if the conic model is suitable to be used. Otherwise, we construct a new quadratic model or two other new approximation models to generate the approximate optimal stepsize for gradient method. We analyze the convergence of the proposed method under some suitable conditions. Numerical results show the proposed method is very promising. 相似文献
18.
We consider the expected residual minimization (ERM) formulation of stochastic linear complementarity problem (SLCP). By employing the Barzilai–Borwein (BB) stepsize and active set strategy, we present a BB type method for solving the ERM problem. The global convergence of the proposed method is proved under mild conditions. Preliminary numerical results show that the method is promising. 相似文献
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20.
基于修正拟牛顿方程,利用Goldstein-Levitin-Polyak(GLP)投影技术,建立了求解带凸集约束的优化问题的两阶段步长非单调变尺度梯度投影算法,证明了算法的全局收敛性和一定条件下的Q超线性收敛速率.数值结果表明新算法是有效的,适合求解大规模问题. 相似文献