共查询到18条相似文献,搜索用时 62 毫秒
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本文提出了一种求解带二次约束和线性约束的二次规划的分支定界算法.在算法中,我们运用Lipschitz条件来确定目标函数和约束函数的在每个n矩形上的上下界,对于n矩形的分割,我们采用选择n矩形最长边的二分法,同时我们采用了一些矩形删除技术,在不大幅增加计算量的前提下,起到了加速算法收敛的效果.从理论上我们证明了算法的收敛性,同时数值实验表明该算法是有效的. 相似文献
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一类改进的非凸二次规划有效集方法修乃华(河北师范学院数学系)ACLASSOFIMPROVEDACTIVESETMETHODSFORNONCONVEXQUADRATICPROGRAMMINGPROBLEM¥XiuNai-hua(Dept.ofMath.... 相似文献
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边界约束非凸二次规划问题的分枝定界方法 总被引:2,自引:0,他引:2
本文是研究带有边界约束非凸二次规划问题,我们把球约束二次规划问题和线性约束凸二次规划问题作为子问题,分明引用了它们的一个求整体最优解的有效算法,我们提出几种定界的紧、松驰策略,给出了求解原问题整体最优解的分枝定界算法,并证明了该算法的收敛性,不同的定界组合就可以产生不同的分枝定界算法,最后我们简单讨论了一般有界凸域上非凸二次规划问题求整体最优解的分枝与定界思想。 相似文献
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求非凸二次约束二次规划问题全局解的线性化方法 总被引:1,自引:0,他引:1
1引言 考虑如下非凸二次规划的全局优化问题: (QP):{min xTQox doTx,s.t.xTQix ditx≤bi,i=1,…,m,x∈S={x∈Rn:l≤x≤u}, 其中Qo,Qi是n阶实对称矩阵,do,di∈Rn,bi∈R,i=1,…,m;l=(l1,…,ln)T,u=(u1,…,un)T . 相似文献
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本文提出一类基于DC分解的非凸二次规划问题SDP松弛方法,并通过求解一个二阶锥问题得到原问题的近似最优解.我们首先对非凸二次目标函数进行DC分解,然后利用线性下逼近得到一个凸二次松弛问题,而最优的DC分解可通过求解一个SDP问题得到.数值试验表明,基于DC分解的SDP近似解平均优于经典SDP松弛和随机化方法产生的近似解。 相似文献
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本文给出了无界域上不定二次规划一个算法 ,该算法将不定二次规划转化为一系列凸二次规划 ,并证明了算法的收敛性 . 相似文献
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本文给出确定线性约束0-1二次规划问题最优值下界的方法,该方法结合McBride和Yormark的思想和总体优化中定下界的方法,证明了所定的界较McBride和Yormark的要好.求解线性约束0-1二次规划问题的分支定界算法可以利用本文的定界技术. 相似文献
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Hong-Xuan Huang Panos M. Pardalos Oleg A. Prokopyev 《Computational Optimization and Applications》2006,33(2-3):187-208
In this paper several equivalent formulations for the quadratic binary programming problem are presented. Based on these formulations
we describe four different kinds of strategies for estimating lower bounds of the objective function, which can be integrated
into a branch and bound algorithm for solving the quadratic binary programming problem. We also give a theoretical explanation
for forcing rules used to branch the variables efficiently, and explore several properties related to obtained subproblems.
From the viewpoint of the number of subproblems solved, new strategies for estimating lower bounds are better than those used
before. A variant of a depth-first branch and bound algorithm is described and its numerical performance is presented. 相似文献
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Global Optimization Techniques for Solving the General Quadratic Integer Programming Problem 总被引:3,自引:0,他引:3
Nguyen Van Thoai 《Computational Optimization and Applications》1998,10(2):149-163
We consider the problem of minimizing a general quadratic function over a polytope in the n-dimensional space with integrality restrictions on all of the variables. (This class of problems contains, e.g., the quadratic 0-1 program as a special case.) A finite branch and bound algorithm is established, in which the branching procedure is the so-called integral rectangular partition, and the bound estimation is performed by solving a concave programming problem with a special structure. Three methods for solving this special concave program are proposed. 相似文献
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本文对一类非凸规划问题(NP)给出一确定性全局优化算法.这类问题包括:在非凸的可行域上极小化有限个带指数的线性函数乘积的和与差,广义线性多乘积规划,多项式规划等.通过利用等价问题和线性化技巧提出的算法收敛到问题(NP)的全局极小. 相似文献
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We apply a linearization technique for nonconvex quadratic problems with box constraints. We show that cutting plane algorithms can be designed to solve the equivalent problems which minimize a linear function over a convex region. We propose several classes of valid inequalities of the convex region which are closely related to the Boolean quadric polytope. We also describe heuristic procedures for generating cutting planes. Results of preliminary computational experiments show that our inequalities generate a polytope which is a fairly tight approximation of the convex region. 相似文献
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Ivo Nowak 《Journal of Global Optimization》1999,14(4):357-364
The paper describes a method for computing a lower bound of the global minimum of an indefinite quadratic form over a simplex. The bound is derived by computing an underestimator of the convex envelope by solving a semidefinite program (SDP). This results in a convex quadratic program (QP). It is shown that the optimal value of the QP is a lower bound of the optimal value of the original problem. Since there exist fast (polynomial time) algorithms for solving SDP's and QP's the bound can be computed in reasonable time. Numerical experiments indicate that the relative error of the bound is about 10 percent for problems up to 20 variables, which is much better than a known SDP bound. 相似文献
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基于粒子群算法的非线性二层规划问题的求解算法 总被引:3,自引:0,他引:3
粒子群算法(Particle Swarm Optimization,PSO)是一种新兴的优化技术,其思想来源于人工生命和演化计算理论。PSO通过粒子追随自己找到的最好解和整个群的最好解来完成优化。该算法简单易实现,可调参数少,已得到了广泛研究和应用。本文根据该算法能够有效的求出非凸数学规划全局最优解的特点,对非线性二层规划的上下层问题求解,并根据二层规划的特点,给出了求解非线性二层规划问题全局最优解的有效算法。数值计算结果表明该算法有效。 相似文献
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Canonical Duality Theory and Solutions to Constrained Nonconvex Quadratic Programming 总被引:6,自引:2,他引:4
David Yang Gao 《Journal of Global Optimization》2004,29(4):377-399
This paper presents a perfect duality theory and a complete set of solutions to nonconvex quadratic programming problems subjected to inequality constraints. By use of the canonical dual transformation developed recently, a canonical dual problem is formulated, which is perfectly dual to the primal problem in the sense that they have the same set of KKT points. It is proved that the KKT points depend on the index of the Hessian matrix of the total cost function. The global and local extrema of the nonconvex quadratic function can be identified by the triality theory [11]. Results show that if the global extrema of the nonconvex quadratic function are located on the boundary of the primal feasible space, the dual solutions should be interior points of the dual feasible set, which can be solved by deterministic methods. Certain nonconvex quadratic programming problems in {\open {R}}^{n} can be converted into a dual problem with only one variable. It turns out that a complete set of solutions for quadratic programming over a sphere is obtained as a by-product. Several examples are illustrated. 相似文献