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By means of a conjugate gradient strategy, we propose a trust region method for unconstrained optimization problems. The search direction is an adequate combination of the conjugate gradient direction and the trust-region direction. The global convergence and the quadratic convergence of this method are established under suitable conditions. Numerical results show that the presented method is competitive to the trust region method and the conjugate gradient method. 相似文献
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本文通过结合牛顿法与PRP共轭梯度法提出一修正PRP方法,新方法中包含了二阶导数信息,在适当的假设下算法全局收敛,数值算例表明了算法的有效性. 相似文献
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Gonglin Yuan 《Numerical Functional Analysis & Optimization》2013,34(8):914-937
Mathematical programming is a rich and well-developed area in operations research. Nevertheless, there remain many challenging problems in this area, one of which is the large-scale optimization problem. In this article, a modified Hestenes and Stiefel (HS) conjugate gradient (CG) algorithm with a nonmonotone line search technique is presented. This algorithm possesses information about not only the gradient value but also the function value. Moreover, the sufficient descent condition holds without any line search. The global convergence is established for nonconvex functions under suitable conditions. Numerical results show that the proposed algorithm is advantageous to existing CG methods for large-scale optimization problems. 相似文献
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本文我们讨论了一簇共轭梯度法,它可被看作是FR法和DY法的凸组合.我们提出了两种Armijo型线搜索,并在这两种线搜索下,讨论了共轭梯度法簇的全局收敛性. 相似文献
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Gonglin Yuan Xiwen Lu Zengxin Wei 《Journal of Computational and Applied Mathematics》2009,233(2):519-530
A modified conjugate gradient method is presented for solving unconstrained optimization problems, which possesses the following properties: (i) The sufficient descent property is satisfied without any line search; (ii) The search direction will be in a trust region automatically; (iii) The Zoutendijk condition holds for the Wolfe–Powell line search technique; (iv) This method inherits an important property of the well-known Polak–Ribière–Polyak (PRP) method: the tendency to turn towards the steepest descent direction if a small step is generated away from the solution, preventing a sequence of tiny steps from happening. The global convergence and the linearly convergent rate of the given method are established. Numerical results show that this method is interesting. 相似文献
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本文对于无约束最优化问题提出了一个新的信赖域方法。在该算法中采用的是线性模型,并且当试探步不成功的时候,采用线性搜索,从而减少了计算量。文中证明了在适当的条件下算法的全局收敛性。 相似文献
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凸约束优化问题的带记忆模型信赖域算法 总被引:1,自引:0,他引:1
本文我们考虑求解凸约束优化问题的信赖域方法 .与传统的方法不同 ,我们信赖域子问题的逼近模型中包括过去迭代点的信息 ,该模型使我们可以从更全局的角度来求得信赖域试探步 ,从而避免了传统信赖域方法中试探步的求取完全依赖于当前点的信息而过于局部化的困难 .全局收敛性的获得是依靠非单调技术来保证的 相似文献
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Jin-yanFan Wen-baoAi Qun-yingZhang 《计算数学(英文版)》2004,22(6):865-872
In this paper, we present a new line search and trust region algorithm for unconstrained optimization problem with the trust region radius converging to zero. The new trust region algorithm performs a backtracking line search from the failed, point instead of resolving the subproblem when the trial step results in an increase in the objective function. We show that the algorithm preserves the convergence properties of the traditional trust region algorithms. Numerical results are also given. 相似文献
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A modified PRP conjugate gradient method 总被引:4,自引:0,他引:4
This paper gives a modified PRP method which possesses the global convergence of nonconvex function and the R-linear convergence
rate of uniformly convex function. Furthermore, the presented method has sufficiently descent property and characteristic
of automatically being in a trust region without carrying out any line search technique. Numerical results indicate that the
new method is interesting for the given test problems.
This work is supported by Guangxi University SF grands X061041 and China NSF grands 10761001. 相似文献
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基于J.M.Peng研究一类变分不等式问题(简记为VIP)时所提出的价值函数,本文提出了求解强单调的VIP的一个新的信赖域算法。和已有的处理VIP的信赖域方法不同的是:它在每步迭代时,不必求解带信赖域界的子问题,仅解一线性方程组而求得试验步。这样,计算的复杂性一般来说可降低。在通常的假设条件下,文中还证明了算法的整体收敛性。最后,在梯度是半光滑和约束是矩形域的假设下,该算法还是超线性收敛的。 相似文献
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本文利用一个修正的BFGS公式,提出了一个结合Armijo线搜索条件技术的BFGS信赖域方法,并在一定条件下证明了该方法的全局收敛性和超线性收敛性.初步的数值实验结果表明该方法是有效的. 相似文献
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本文对带线性等式约束的LC^1优化问题提出了一个新的ODE型信赖域算法,它在每一次迭代时,不必求解带信赖域界的子问题,仅解一线性方程组而求得试验步。从而可以降低计算的复杂性,提高计算效率,在一定的条件下,文中还证明了该算法是超线性收敛的。 相似文献
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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
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Conjugate gradient methods are a class of important methods for unconstrained optimization, especially when the dimension
is large. This paper proposes a new conjugacy condition, which considers an inexact line search scheme but reduces to the
old one if the line search is exact. Based on the new conjugacy condition, two nonlinear conjugate gradient methods are constructed.
Convergence analysis for the two methods is provided. Our numerical results show that one of the methods is very efficient
for the given test problems.
Accepted 15 September 2000. Online publication 8 December 2000. 相似文献
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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
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In this article, without computing exact gradient and Jacobian, we proposed a derivative-free Polak-Ribière-Polyak (PRP) method for solving nonlinear equations whose Jacobian is symmetric. This method is a generalization of the classical PRP method for unconstrained optimization problems. By utilizing the symmetric structure of the system sufficiently, we prove global convergence of the proposed method with some backtracking type line search under suitable assumptions. Moreover, we extend the proposed method to nonsmooth equations by adopting the smoothing technique. We also report some numerical results to show its efficiency. 相似文献