共查询到17条相似文献,搜索用时 125 毫秒
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利用广义投影矩阵,对求解无约束规划的三项记忆梯度算法中的参数给一条件,确定它们的取值范围,以保证得到目标函数的三项记忆梯度广义投影下降方向,建立了求解非线性等式和不等式约束优化问题的三项记忆梯度广义投影算法,并证明了算法的收敛性.同时给出了结合FR,PR,HS共轭梯度参数的三项记忆梯度广义投影算法,从而将经典的共轭梯度算法推广用于求解约束规划问题.数值例子表明算法是有效的. 相似文献
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线性约束最优化的一个共轭投影梯度法 总被引:1,自引:0,他引:1
本结合共轭梯度法及梯度投影法的思想,建立线性等式约束最优化的一个新算法,称之为共轭投影梯度法。分别对二次凸目标函数和一般目标函数分析和论证了算法的重要性质和收敛性。 相似文献
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梯度投影法是一类有效的约束最优化算法,在最优化领域中占有重要的地位.但是,梯度投影法所采用的投影是正交投影,不包含目标函数和约束函数的二阶导数信息·因而;收敛速度不太令人满意.本文介绍一种共轭投影概念,利用共轭投影构造了一般线性或非线性约束下的共轭投影变尺度算法,并证明了算法在一定条件下具有全局收敛性.由于算法中的共轭投影恰当地包含了目标函数和约束函数的二阶导数信息,因而收敛速度有希望加快.数值试验的结果表明算法是有效的. 相似文献
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解带线性或非线性约束最优化问题的三项记忆梯度Rosen投影算法 总被引:2,自引:0,他引:2
利用Rosen投影矩阵,建立求解带线性或非线性不等式约束优化问题的三项记忆梯度Rosen投影下降算法,并证明了算法的收敛性.同时给出了结合FR,PR,HS共轭梯度参数的三项记忆梯度Rosen投影算法,从而将经典的共轭梯度法推广用于求解约束规划问题.数值例子表明算法是有效的。 相似文献
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一个新的共轭投影梯度算法及其超线性收敛性 总被引:7,自引:0,他引:7
利用共轭投影梯度技巧,结合SQP算法的思想,建立了一个具有显示搜索方向的新算法,在适当的条件下,证明算法是全局收敛和强收敛的,且具有超线性收敛性,最后数值实验表明算法是有效的。 相似文献
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借助谱梯度法和HS共轭梯度法的结构, 建立一种求解非线性单调方程组问题的谱HS投影算法. 该算法继承了谱梯度法和共轭梯度法储存量小和计算简单的特征,
且不需要任何导数信息, 因此它适应于求解大规模非光滑的非线性单调方程组问题. 在适当的条件下, 证明了该算法的收敛性, 并通过数值实验表明了该算法的有效性. 相似文献
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WeiWang Lian-shengZhang Yi-fanXu 《计算数学(英文版)》2005,23(2):217-224
A revised conjugate gradient projection method for nonlinear inequality constrained optimization problems is proposed in the paper, since the search direction is the combination of the conjugate projection gradient and the quasi-Newton direction. It has two merits. The one is that the amount of computation is lower because the gradient matrix only needs to be computed one time at each iteration. The other is that the algorithm is of global convergence and locally superlinear convergence without strict complementary condition under some mild assumptions. In addition the search direction is explicit. 相似文献
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本文研究了不等式约束优化问题.利用共轭投影梯度方法,获得了一个投影变尺度型算法.在适当的条件下,证明算法是全局收敛且具有超线性收敛性. 相似文献
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《Optimization》2012,61(10):1631-1648
ABSTRACTIn this paper, we develop a three-term conjugate gradient method involving spectral quotient, which always satisfies the famous Dai-Liao conjugacy condition and quasi-Newton secant equation, independently of any line search. This new three-term conjugate gradient method can be regarded as a variant of the memoryless Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method with regard to spectral quotient. By combining this method with the projection technique proposed by Solodov and Svaiter in 1998, we establish a derivative-free three-term projection algorithm for dealing with large-scale nonlinear monotone system of equations. We prove the global convergence of the algorithm and obtain the R-linear convergence rate under some mild conditions. Numerical results show that our projection algorithm is effective and robust, and is more competitive with the TTDFP algorithm proposed Liu and Li [A three-term derivative-free projection method for nonlinear monotone system of equations. Calcolo. 2016;53:427–450]. 相似文献
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The recent designed non-linear conjugate gradient method of Dai and Kou [SIAM J Optim. 2013;23:296–320] is very efficient currently in solving large-scale unconstrained minimization problems due to its simpler iterative form, lower storage requirement and its closeness to the scaled memoryless BFGS method. Just because of these attractive properties, this method was extended successfully to solve higher dimensional symmetric non-linear equations in recent years. Nevertheless, its numerical performance in solving convex constrained monotone equations has never been explored. In this paper, combining with the projection method of Solodov and Svaiter, we develop a family of non-linear conjugate gradient methods for convex constrained monotone equations. The proposed methods do not require the Jacobian information of equations, and even they do not store any matrix in each iteration. They are potential to solve non-smooth problems with higher dimensions. We prove the global convergence of the class of the proposed methods and establish its R-linear convergence rate under some reasonable conditions. Finally, we also do some numerical experiments to show that the proposed methods are efficient and promising. 相似文献
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In this study, a modified spectral conjugate gradient projection method is presented to solve total variation image restoration, which is transferred into the nonlinear constrained optimization with the closed constrained set. The global convergence of the proposed scheme is analyzed. In the end, some numerical results illustrate the efficiency of this method. 相似文献
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陈香萍 《数学的实践与认识》2017,(13):168-175
推广了一种修正的CG_DESCENT共轭梯度方法,并建立了一种有效求解非线性单调方程组问题的无导数投影算法.在适当的线搜索条件下,证明了算法的全局收敛性.由于新算法不需要借助任何导数信息,故它适应于求解大规模非光滑的非线性单调方程组问题.大量的数值试验表明,新算法对给定的测试问题是有效的. 相似文献