共查询到19条相似文献,搜索用时 78 毫秒
1.
2.
在修正PRP共轭梯度法的基础上,提出了求解无约束优化问题的一个充分下降共轭梯度算法,证明了算法在Wolfe线搜索下全局收敛,并用数值实验表明该算法具有较好的数值结果. 相似文献
3.
4.
Polak-Ribière-Polak (PRP)方法是经典共轭梯度法中数值表现较好的方法之一.结合Wolfe非精确线搜索准则对PRP公式进行改进,从而产生新的共轭参数,并基于新共轭参数设计新的谱参数,引入重启条件并构造新的重启方向,进而建立一个带重启步的谱共轭梯度算法.在常规假设及强Wolfe非精确线搜索步长准则下,... 相似文献
5.
提出了一类新的非单调谱共轭梯度方法.该方法通过引入混合因子,将HS方法和PRP方法结合得到共轭系数的新的选取方式.以此为基础,通过合适地选取谱系数保证了所有搜索方向不依赖于线搜索条件,恒为充分下降方向.其次,该方法还修正了Zhang和Hager提出的非单调线搜索规则,在更弱的假设条件下证明了全局收敛性.数值试验说明了该方法的计算性能优良. 相似文献
6.
7.
本文对半定规划(SDP)的最优性条件提出一价值函数并研究其性质.基此,提出半定规划的PRP+共轭梯度法.为得到PRP+共轭梯度法的收敛性,提出一Armijo-型线搜索.无需水平集有界及迭代点列聚点的存在,算法全局收敛. 相似文献
8.
为解决大规模无约束优化问题,该文结合WYL共轭梯度法和谱共轭梯度法,给出了一种WYL型谱共轭梯度法.在不依赖于任何线搜索的条件下,该方法产生的搜索方向均满足充分下降性,且在强Wolfe线搜索下证明了该方法的全局收敛性.与WYL共轭梯度法的收敛性相比,WYL型谱共轭梯度法推广了线搜索中参数σ的取值范围.最后,相应的数值结果表明了该方法是有效的. 相似文献
9.
提出了求解无约束优化问题的新型DL共轭梯度方法. 同已有方法不同之处在于,该方法构造了一种修正的Armijo线搜索规则,它不仅能给出当前迭代步步长, 而且还能同时确定计算下一步搜索方向时需要用到的共轭参数值. 在较弱的条件下, 建立了算法的全局收敛性理论. 数值试验表明,新型共轭梯度算法比同类方法具有更好的计算效率. 相似文献
10.
强Wolfe条件不能保证标准CD共轭梯度法全局收敛.本文通过建立新的共轭参数,提出无约束优化问题的一个新谱共轭梯度法,该方法在精确线搜索下与标准CD共轭梯度法等价,在标准wolfe线搜索下具有下降性和全局收敛性.初步的数值实验结果表明新方法是有效的,适合于求解非线性无约束优化问题. 相似文献
11.
In this paper, a modified formula for βk^PRP is proposed for the conjugate gradient method of solving unconstrained optimization problems. The value of βk^PRP keeps nonnegative independent of the line search. Under mild conditions, the global convergence of modified PRP method with the strong Wolfe-Powell line search is established. Preliminary numerical results show that the modified method is efficient. 相似文献
12.
《Optimization》2012,61(2):163-179
In this article, we consider the global convergence of the Polak–Ribiére–Polyak conjugate gradient method (abbreviated PRP method) for minimizing functions that have Lipschitz continuous partial derivatives. A novel form of non-monotone line search is proposed to guarantee the global convergence of the PRP method. It is also shown that the PRP method has linear convergence rate under some mild conditions when the non-monotone line search reduces to a related monotone line search. The new non-monotone line search needs to estimate the Lipschitz constant of the gradients of objective functions, for which two practical estimations are proposed to help us to find a suitable initial step size for the PRP method. Numerical results show that the new line search approach is efficient in practical computation. 相似文献
13.
In this paper, a new spectral PRP conjugate gradient algorithm has been developed for solving unconstrained optimization problems, where the search direction was a kind of combination of the gradient and the obtained direction, and the steplength was obtained by the Wolfe-type inexact line search. It was proved that the search direction at each iteration is a descent direction of objective function. Under mild conditions, we have established the global convergence theorem of the proposed method. Numerical results showed that the algorithm is promising, particularly, compared with the existing several main methods. 相似文献
14.
Weijun Zhou 《Optimization Letters》2013,7(6):1367-1372
To guarantee global convergence of the standard (unmodified) PRP nonlinear conjugate gradient method for unconstrained optimization, the exact line search or some Armijo type line searches which force the PRP method to generate descent directions have been adopted. In this short note, we propose a non-descent PRP method in another way. We prove that the unmodified PRP method converges globally even for nonconvex minimization by the use of an approximate descent inexact line search. 相似文献
15.
It is well known that global convergence has not been established for the Polak-Ribière-Polyak (PRP) conjugate gradient method using the standard Wolfe conditions. In the convergence analysis of PRP method with Wolfe line search, the (sufficient) descent condition and the restriction βk?0 are indispensable (see [4,7]). This paper shows that these restrictions could be relaxed. Under some suitable conditions, by using a modified Wolfe line search, global convergence results were established for the PRP method. Some special choices for βk which can ensure the search direction’s descent property were also discussed in this paper. Preliminary numerical results on a set of large-scale problems were reported to show that the PRP method’s computational efficiency is encouraging. 相似文献
16.
It is well-known that the HS method and the PRP method may not converge for nonconvex optimization even with exact line search. Some globalization techniques have been proposed, for instance, the PRP+ globalization technique and the Grippo-Lucidi globalization technique for the PRP method. In this paper, we propose a new efficient globalization technique for general nonlinear conjugate gradient methods for nonconvex minimization. This new technique utilizes the information of the previous search direction sufficiently. Under suitable conditions, we prove that the nonlinear conjugate gradient methods with this new technique are globally convergent for nonconvex minimization if the line search satisfies Wolfe conditions or Armijo condition. Extensive numerical experiments are reported to show the efficiency of the proposed technique. 相似文献
17.
Although the study of global convergence of the Polak–Ribière–Polyak (PRP), Hestenes–Stiefel (HS) and Liu–Storey (LS) conjugate
gradient methods has made great progress, the convergence of these algorithms for general nonlinear functions is still erratic,
not to mention under weak conditions on the objective function and weak line search rules. Besides, it is also interesting
to investigate whether there exists a general method that converges under the standard Armijo line search for general nonconvex
functions, since very few relevant results have been achieved. So in this paper, we present a new general form of conjugate
gradient methods whose theoretical significance is attractive. With any formula β
k
≥ 0 and under weak conditions, the proposed method satisfies the sufficient descent condition independently of the line search
used and the function convexity, and its global convergence can be achieved under the standard Wolfe line search or even under
the standard Armijo line search. Based on this new method, convergence results on the PRP, HS, LS, Dai–Yuan–type (DY) and
Conjugate–Descent–type (CD) methods are established. Preliminary numerical results show the efficiency of the proposed methods. 相似文献
18.
本文在文献[1]中提出了一类新共轭梯度法的基础上,给出求解无约束优化问题的两类新的非线性下降共轭梯度法,此两类方法在无任何线搜索下,能够保证在每次迭代中产生下降方向.对一般非凸函数,我们在Wolfe线搜索条件下证明了两类新方法的全局收敛性. 相似文献
19.
Wanyou Cheng 《Numerical Functional Analysis & Optimization》2013,34(11-12):1217-1230
In this paper, by the use of the project of the PRP (Polak–Ribiére–Polyak) conjugate gradient direction, we develop a PRP-based descent method for solving unconstrained optimization problem. The method provides a sufficient descent direction for the objective function. Moreover, if exact line search is used, the method reduces to the standard PRP method. Under suitable conditions, we show that the method with some backtracking line search or the generalized Wolfe-type line search is globally convergent. We also report some numerical results and compare the performance of the method with some existing conjugate gradient methods. The results show that the proposed method is efficient. 相似文献