共查询到20条相似文献,搜索用时 296 毫秒
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梯度法是求解无约束最优化的一类重要方法.步长选取的好坏与梯度法的数值表现息息相关.注意到BB步长隐含了目标函数的二阶信息,本文将BB法与信赖域方法相结合,利用BB步长的倒数去近似目标函数的Hesse矩阵,同时利用信赖域子问题更加灵活地选取梯度法的步长,给出求解无约束最优化问题的单调和非单调信赖域BB法.在适当的假设条件下,证明了算法的全局收敛性.数值试验表明,与已有的求解无约束优化问题的BB类型的方法相比,非单调信赖域BB法中e_k=‖x_k-x~*‖的下降呈现更明显的阶梯状和单调性,因此收敛速度更快. 相似文献
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该文给出了一个求解非线性系统的信赖域方法.主要思想是通过引入松弛变量,将问题等价地转化为带非负约束的最优化问题.作者利用有效集策略,在每次迭代中只需求解一个低维的信赖域子问题,该信赖域子问题是通过截断共轭梯度法来近似求解的.在较弱的条件下,获得了一个更一般的收敛性结果. 相似文献
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提出了一类新的求解无约束最优化问题的新拟牛顿非单调信赖域算法.采用加权的r_k用以调整信赖域半径,在适当的条件下,证明了算法的全局收敛性.数值结果表明算法的有效性. 相似文献
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一类带非单调线搜索的信赖域算法 总被引:1,自引:0,他引:1
通过将非单调Wolfe线搜索技术与传统的信赖域算法相结合,我们提出了一类新的求解无约束最优化问题的信赖域算法.新算法在每一迭代步只需求解一次信赖域子问题,而且在每一迭代步Hesse阵的近似都满足拟牛顿条件并保持正定传递.在一定条件下,证明了算法的全局收敛性和强收敛性.数值试验表明新算法继承了非单调技术的优点,对于求解某... 相似文献
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一类拟牛顿非单调信赖域算法及其收敛性 总被引:2,自引:0,他引:2
本文提出了一类求解无约束最优化问题的非单调信赖域算法.将非单调Wolfe线搜索技术与信赖域算法相结合,使得新算-法不仅不需重解子问题,而且在每步迭代都满足拟牛顿方程同时保证目标函数的近似Hasse阵Bk的正定性.在适当的条件下,证明了此算法的全局收敛性.数值结果表明该算法的有效性. 相似文献
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R. W. Chaney 《Journal of Optimization Theory and Applications》1976,20(3):269-295
The method of centers is a well-known method for solving nonlinear programming problems having inequality constraints. Pironneau and Polak have recently presented a new version of this method. In the new method, the direction of search is obtained, at each iteration, by solving a convex quadratic programming problem. This direction finding subprocedure is essentially insensitive to the dimension of the space on which the problem is defined. Moreover, the method of Pironneau and Polak is known to converge linearly for finite-dimensional convex programs for which the objective function has a positive-definite Hessian near the solution (and for which the functions involved are twice continuously differentiable). In the present paper, the method and a completely implementable version of it are shown to converge linearly for a very general class of finite-dimensional problems; the class is determined by a second-order sufficiency condition and includes both convex and nonconvex problems. The arguments employed here are based on the indirect sufficiency method of Hestenes. Furthermore, the arguments can be modified to prove linear convergence for a certain class of infinite-dimensional convex problems, thus providing an answer to a conjecture made by Pironneau and Polak. 相似文献
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A remark on a regularity assumption for the mathematical programming problem in Banach spaces 总被引:3,自引:0,他引:3
J. Zowe 《Journal of Optimization Theory and Applications》1978,25(3):375-381
This paper deals with a recently proposed Slater-like regularity condition for the mathematical programming problem in infinite-dimensional vector spaces (Ref. 1). The attractive feature of this constraint qualification is the fact that it can be considered as a condition only on theactive part of the constraint. We prove that the studied regularity condition is equivalent to the regularity assumption normally used in the study of the mathematical programming problem in infinite-dimensional vector spaces. 相似文献
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Hu Ying 《Applied Mathematics and Optimization》1991,24(1):257-271
In this paper the problem ofN-person infinite-dimensional stochastic differential games governed by semilinear stochastic evolution control systems is discussed. First the minimax principle which is the necessary condition for the existence of open-loop Nash equilibrium is proved. Then the necessary and sufficient conditions of open-loop and closed-loop Nash equilibrium for linear quadratic infinite-dimensional stochastic differential games are derived. 相似文献
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研究一类无限维非线性互补问题的光滑化牛顿法.借助于非线性互补函数,将无限维非线性互补问题转化为一个非光滑算子方程.构造光滑算子逼近非光滑算子,在光滑逼近算子满足方向可微相容性的条件下,证明了光滑化牛顿法具有超线性收敛性. 相似文献
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Boris Yu. Sternin 《Central European Journal of Mathematics》2011,9(4):814-832
We consider a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold. Ellipticity condition and Fredholm property for elliptic operators are obtained. This class
of operators is studied using pseudodifferential uniformization, which reduces the problem to a pseudodifferential operator
acting in sections of infinite-dimensional bundles. 相似文献
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We present a separation theorem in which the classic interior is replaced by the quasirelative interior. We apply this result to a constrained problem in the infinite-dimensional convex case, making use of a condition replacing the standard Slater condition, which in some cases can fail. 相似文献
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The infinite-dimensional versions of the linear quadratic cost control problem and of the linear filtering problem lead to an infinite-dimensional Riccati equation with unbounded operators. Existence and uniqueness theorems for mild solutions of this Riccati equation are established using a sequential approach based on approximating controllers for the linear quadratic cost control problem. By using a semigroup and evolution equation approach, the results are valid for a large class of unbounded operators and, hence, are applicable to many linear infinite-dimensional control systems. 相似文献
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The aim of this paper is to identify the volatility function in Dupire’s equation from given option prices. This inverse problem is formulated as an infinite-dimensional minimization problem with PDE constraints. The computational cost of solving the discretized problem on a fine discretization level is expensive. A multi-grid method is proposed to explore the hierarchical structures of discretized problems on different levels. Computational examples are presented to demonstrate the efficiency of our method. 相似文献
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In this paper a Basic Constraint Qualification is introduced for a nonconvex infinite-dimensional vector optimization problem extending the usual one from convex programming assuming the Hadamard differentiability of the maps. Corresponding KKT conditions are established by considering a decoupling of the constraint cone into half-spaces. This extension leads to generalized KKT conditions which are finer than the usual abstract multiplier rule. A second constraint qualification expressed directly in terms of the data is also introduced, which allows us to compute the contingent cone to the feasible set and, as a consequence, it is proven that this condition is a particular case of the first one. Relationship with other constraint qualifications in infinite-dimensional vector optimization, specially with the Kurcyuscz-Robinson-Zowe constraint qualification, are also given. 相似文献
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Tullio Zolezzi 《Numerical Functional Analysis & Optimization》2013,34(12):1381-1404
The condition number of a given mathematical problem is often related to the reciprocal of its distance from ill-conditioning. Such a property is proved here in the infinite-dimensional setting for linear-quadratic convex optimization of two types: linearly constrained convex quadratic problems, and minimum norm least squares solutions. A uniform version of such theorem is obtained in both cases for suitably equi-bounded classes of optimization problems. An application to the conditioning of a Ritz method is presented. For least squares problems it is shown that the semi-Fredholm property of the operators involved determines the validity of a condition number theorem. 相似文献