共查询到20条相似文献,搜索用时 156 毫秒
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信赖域算法是求解无约束优化问题的一种有效的算法.对于该算法的子问题,本文将原来目标函数的二次模型扩展成四次张量模型,提出了一个带信赖域约束的四次张量模型优化问题的求解算法.该方法的最大特点是:不仅在张量模型的非稳定点可以得到下降方向及相应的迭代步长,而且在非局部极小值点的稳定点也可以得到下降方向及相应的迭代步长,从而在算法产生的迭代点列中存在一个子列收敛到信赖域子问题的局部极小值点. 相似文献
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首先利用Lagrange对偶 ,将球约束凸二次规划问题转化为无约束优化问题 ,然后运用单纯形法求解无约束优化问题 ,从而获得原问题的最优解 相似文献
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带非线性不等式约束优化问题的信赖域算法 总被引:1,自引:0,他引:1
借助于KKT条件和NCP函数,提出了求解带非线性不等式约束优化问题的信赖域算法.该算法在每一步迭代时,不必求解带信赖域界的二次规划子问题,仅需求一线性方程组系统.在适当的假设条件下,它还是整体收敛的和局部超线性收敛的.数值实验结果表明该方法是有效的. 相似文献
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提出一个基于滤子技术的填充函数算法, 用于求解带箱式约束的非凸全局优化问题. 填充函数算法是求解全局优化问题的有效方法之一, 而滤子技术以其良好的数值效果广泛应用于局部优化算法中. 为优化填充函数方法, 应用滤子来监控迭代过程. 首先给出一个新的填充函数并讨论了其特性, 在此基础上提出了理论算法及算法性质. 最后列出数值实验结果以说明算法的有效性. 相似文献
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主要研究了非增值型凸二次双层规划的一种有效求解算法。首先利用数学规划的对偶理论,将所求双层规划转化为一个下层只有一个无约束凸二次子规划的双层规划问题.然后根据两个双层规划的最优解和最优目标值之间的关系,提出一种简单有效的算法来解决非增值型凸二次双层规划问题.并通过数值算例的计算结果说明了该算法的可行性和有效性。 相似文献
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Jin-bao Jian 《Journal of Mathematical Analysis and Applications》2010,362(1):34-45
In this paper, a sequential quadratically constrained quadratic programming (SQCQP) method for unconstrained minimax problems is presented. At each iteration the SQCQP method solves a subproblem that involves convex quadratic inequality constraints and a convex quadratic objective function. The global convergence of the method is obtained under much weaker conditions without any constraint qualification. Under reasonable assumptions, we prove the strong convergence, superlinearly and quadratic convergence rate. 相似文献
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一类不可微二次规划逆问题 总被引:1,自引:0,他引:1
本文求解了一类二次规划的逆问题,具体为目标函数是矩阵谱范数与向量无穷范数之和的最小化问题.首先将该问题转化为目标函数可分离变量的凸优化问题,提出用G-ADMM法求解.并结合奇异值阈值算法,Moreau-Yosida正则化算法,matlab优化工具箱的quadprog函数来精确求解相应的子问题.而对于其中一个子问题的精确求解过程中发现其仍是目标函数可分离变量的凸优化问题,由于其变量都是矩阵,所以采用适合多个矩阵变量的交替方向法求解,通过引入新的变量,使其每个子问题的解都具有显示表达式.最后给出采用的G-ADMM法求解本文问题的数值实验.数据表明,本文所采用的方法能够高效快速地解决该二次规划逆问题. 相似文献
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Wu Li 《Mathematical Programming》1996,72(1):17-32
In this paper, we show that an analogue of the classical conjugate gradient method converges linearly when applied to solving
the problem of unconstrained minimization of a strictly convex quadratic spline. Since a strictly convex quadratic program
with simple bound constraints can be reformulated as unconstrained minimization of a strictly convex quadratic spline, the
conjugate gradient method is used to solve the unconstrained reformulation and find the solution of the original quadratic
program. In particular, if the solution of the original quadratic program is nondegenerate, then the conjugate gradient method
finds the solution in a finite number of iterations.
This author's research is partially supported by the NASA/Langley Research Center under grant NCC-1-68 Supplement-15. 相似文献
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Most of the descent methods developed so far suffer from the computational burden due to a sequence of constrained quadratic subproblems which are needed to obtain a descent direction. In this paper we present a class of proximal-type descent methods with a new direction-finding subproblem. Especially, two of them have a linear programming subproblem instead of a quadratic subproblem. Computational experience of these two methods has been performed on two well-known test problems. The results show that these methods are another very promising approach for nondifferentiable convex optimization. 相似文献
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Let S be a compact, weak self-similar perfect set based on a system of weak contractions fj, j=1,…,m each of which is characterized by a variable contraction coefficient j(l) as d(fj(x),fj(y)) j(l)d(x,y), d(x,y)<l, l>0. If the relation ∑mj=1j(l0)<1 holds at at least one point l0, then every nonempty compact metric space is a continuous image of the set S. 相似文献
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Huiling Lin 《Computational Optimization and Applications》2012,53(1):45-89
We present an inexact spectral bundle method for solving convex quadratic semidefinite optimization problems. This method is a first-order method, hence requires much less computational cost in each iteration than second-order approaches such as interior-point methods. In each iteration of our method, we solve an eigenvalue minimization problem inexactly, and solve a small convex quadratic semidefinite program as a subproblem. We give a proof of the global convergence of this method using techniques from the analysis of the standard bundle method, and provide a global error bound under a Slater type condition for the problem in question. Numerical experiments with matrices of order up to 3000 are performed, and the computational results establish the effectiveness of this method. 相似文献
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交替方向法求解带线性约束的变分不等式 总被引:1,自引:0,他引:1
周瑾 《高等学校计算数学学报》1999,21(2):161-169
1引言变分不等式是一个有广泛应用的数学问题,它的一般形式是:确定一个向量,使其满足这里f是一个从到自身的一个映射,S是R中的一个闭凸集.在许多实际问题中集合S往往具有如下结构其中AbK是中的一个简单闭凸集.例如一个正卦限,一个框形约束结构,或者一个球简言之,S是R中的一个超平面与一个简单闭凸集的交.求解问题(1)-(2),往往是通过对线性约束A引人Lagrange乘子,将原问题化为如下的变分不等式:确定使得我们记问题(3)-(4)为VI(F).熟知[3],VI(,F)等价于投影方程其中凡(·)表… 相似文献
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本文考虑一类离散型随机$R_0$ 张量互补问题,利用Fischer-Burmeister函数将问题转化为约束优化问题,并用投影Levenberg-Marquardt方法对其进行了求解。在一般的条件下得到了该方法的全局收敛性,相关的数值实验表明了该方法的有效性。 相似文献