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解一般线性规划逆问题的一个O(n^3L)算法 总被引:3,自引:1,他引:2
本文讨论了一般线性规划逆问题在各种情况下的求解,并基于解凸二次规划的原对偶内点算法,给出了一个O(n3L)算法和一个实用算法. 相似文献
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求解中大规模复杂凸二次整数规划问题的新型分枝定界算法 总被引:1,自引:0,他引:1
针对现有分枝定界算法在求解高维复杂二次整数规划问题时所存在的诸多不足,本文通过充分挖掘二次整数规划问题的结构特性来设计选择分枝变量与分枝方向的新方法,并将HNF算法与原问题松弛问题的求解相结合来寻求较好的初始整数可行解,由此导出可用于有效求解中大规模复杂二次整数规划问题的改进型分枝定界算法.数值试验结果表明所给算法大大改进了已有相关的分枝定界算法,并具有较好的稳定性与广泛的适用性. 相似文献
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本文将正交校正共轭梯度法推广来解只有部分变量带非负约束而其它变量无约束的严格凸二次规划,所建立的新算法的优点是:在迭代过程中,不用求逆矩阵,这样能保持矩阵的稀疏性,数值结果表明:算法对大规模稀疏二次规划问题是可行和有效的. 相似文献
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根据广义乘子法的思想,将具有等式约束和非负约束的凸二次规划问题转化只有非负约束的简单凸二次规划,通过简单凸二次规划来得到解等式约束一非负约束的凸二次规划新算法,新算法不用求逆矩阵,这样可充分保持矩阵的稀疏性,用来解大规模稀疏问题,数值结果表明:在微机486/33上就能解较大规模的凸二次规划。 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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部分变量带非负约束的严格凸二次规划问题的新算法 总被引:1,自引:0,他引:1
本将正交校正共轭梯度法推广来解只有部分变量带非负约束而其它变量无约束的严格凸二次规划,所建立的新算法的优点是:在迭代过程中,不用求逆矩阵,这样能保持矩阵的稀疏性,数值结果表明,算法对大规模稀疏二次规划问题是可行和有效的。 相似文献
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以下层问题的K-T最优性条件代替下层问题,将线性二层规划转化为相应的单层规划问题,通过分析单层规划可行解集合的结构特征,设计了一种求解线性二层规划全局最优解的割平面算法.数值结果表明所设计的割平面算法是可行、有效的. 相似文献
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In this paper, an inverse complementarity power iteration method (ICPIM) for solving eigenvalue complementarity problems (EiCPs) is proposed. Previously, the complementarity power iteration method (CPIM) for solving EiCPs was designed based on the projection onto the convex cone K. In the new algorithm, a strongly monotone linear complementarity problem over the convex cone K is needed to be solved at each iteration. It is shown that, for the symmetric EiCPs, the CPIM can be interpreted as the well‐known conditional gradient method, which requires only linear optimization steps over a well‐suited domain. Moreover, the ICPIM is closely related to the successive quadratic programming (SQP) via renormalization of iterates. The global convergence of these two algorithms is established by defining two nonnegative merit functions with zero global minimum on the solution set of the symmetric EiCP. Finally, some numerical simulations are included to evaluate the efficiency of the proposed algorithms. 相似文献
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In this study, a numerical solution of the Regularized Long Wave (RLW) equation is obtained using Galerkin finite element method, based on two and three steps Adams Moulton method for the time integration and quadratic trigonometric B-spline functions for the space integration. After two different linearization techniques are applied, the proposed algorithms are tested on the problems of propagation of a solitary wave and interaction of two solitary waves. For the first test problem, the rate of convergence and the running time of the proposed algorithms are computed and the error norm $L_{\infty }$ is used to measure the differences between exact and numerical solutions. The three conservation quantities of the motion are calculated to determine the conservation properties of the proposed algorithms for both of the test problems. 相似文献
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In this paper we study inexact inverse iteration for solving the generalised eigenvalue problem A
x=λM
x. We show that inexact inverse iteration is a modified Newton method and hence obtain convergence rates for various versions
of inexact inverse iteration for the calculation of an algebraically simple eigenvalue. In particular, if the inexact solves
are carried out with a tolerance chosen proportional to the eigenvalue residual then quadratic convergence is achieved. We
also show how modifying the right hand side in inverse iteration still provides a convergent method, but the rate of convergence
will be quadratic only under certain conditions on the right hand side. We discuss the implications of this for the preconditioned
iterative solution of the linear systems. Finally we introduce a new ILU preconditioner which is a simple modification to
the usual preconditioner, but which has advantages both for the standard form of inverse iteration and for the version with
a modified right hand side. Numerical examples are given to illustrate the theoretical results.
AMS subject classification (2000) 65F15, 65F10 相似文献
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Thi Thu Van Nguyen Jean-Jacques Strodiot Van Hien Nguyen 《Journal of Global Optimization》2009,44(2):175-192
In this article we present a new and efficient method for solving equilibrium problems on polyhedra. The method is based on
an interior-quadratic proximal term which replaces the usual quadratic proximal term. This leads to an interior proximal type
algorithm. Each iteration consists in a prediction step followed by a correction step as in the extragradient method. In a
first algorithm each of these steps is obtained by solving an unconstrained minimization problem, while in a second algorithm
the correction step is replaced by an Armijo-backtracking linesearch followed by an hyperplane projection step. We prove that
our algorithms are convergent under mild assumptions: pseudomonotonicity for the two algorithms and a Lipschitz property for
the first one. Finally we present some numerical experiments to illustrate the behavior of the proposed algorithms. 相似文献
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1IntroductionWeconsiderastrictlyconvex(i.e.,positivedefinite)quadraticprogrammingproblemsubjecttoboxconstraints:t-iereA=[aij]isannxnsymmetricpositivedefinitematrix,andb,canddaren-vectors.Letg(x)bethegradient,Ax b,off(x)atx.Withoutlossofgeneralityweassumebothcianddiarefinitenumbers,ci相似文献
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In this paper,a new globally convergent algorithm for nonlinear optimization prablems with equality and inequality constraints is presented. The new algorithm is of SQP type which determines a search direction by solving a quadratic programming subproblem per itera-tion. Some revisions on the quadratic programming subproblem have been made in such a way that the associated constraint region is nonempty for each point x generated by the algorithm, i. e. , the subproblems always have optimal solutions. The new algorithm has two important properties. The computation of revision parameter for guaranteeing the consistency of quadratic sub-problem and the computation of the second order correction step for superlinear convergence use the same inverse of a matrix per iteration, so the computation amount of the new algorithm will not be increased much more than other SQP type algorithms; Another is that the new algorithm can give automatically a feasible point as a starting point for the quadratic subproblems pe 相似文献
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The paper presents a straightforward generalization of the Simplex and the dual method for linear programming to the case of convex quadratic programming. The two algorithms, called the Simplex and the dual method for quadratic programming, are applicable when the matrix of the quadratic part of the objective function, in case this function is to be maximized, is negative definite, negative semi-definite or zero; in the last case the two methods are equivalent to an application of the similar methods for linear programming. The paper gives an exposition of the methods as well as examples and interpretations. The relations with linear programming methods are considered and some starting procedures in case no initial feasible solution is available are presented. 相似文献