共查询到19条相似文献,搜索用时 312 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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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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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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给出了粒子群算法中惯性权值和学习因子的一种简单改进,并将其应用到非凸二次规划的求解中,通过数值试验与现有的求解非凸二次规划问题的分支定界法进行了比较,得到了较好的结果. 相似文献
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In this paper, we present a new sequential quadratically constrained quadratic programming (SQCQP) algorithm, in which a simple updating strategy of the penalty parameter is adopted. This strategy generates nonmonotone penalty parameters at early iterations and only uses the multiplier corresponding to the bound constraint of the quadratically constrained quadratic programming (QCQP) subproblem instead of the multipliers of the quadratic constraints, which will bring some numerical advantages. Furthermore, by using the working set technique, we remove the constraints of the QCQP subproblem that are locally irrelevant, and thus the computational cost could be reduced. Without assuming the convexity of the objective function or the constraints, the algorithm is proved to be globally, superlinearly and quadratically convergent. Preliminary numerical results show that the proposed algorithm is very promising when compared with the tested SQP algorithms. 相似文献
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《Journal of Computational and Applied Mathematics》2012,236(6):1382-1398
In this paper, we present a new sequential quadratically constrained quadratic programming (SQCQP) algorithm, in which a simple updating strategy of the penalty parameter is adopted. This strategy generates nonmonotone penalty parameters at early iterations and only uses the multiplier corresponding to the bound constraint of the quadratically constrained quadratic programming (QCQP) subproblem instead of the multipliers of the quadratic constraints, which will bring some numerical advantages. Furthermore, by using the working set technique, we remove the constraints of the QCQP subproblem that are locally irrelevant, and thus the computational cost could be reduced. Without assuming the convexity of the objective function or the constraints, the algorithm is proved to be globally, superlinearly and quadratically convergent. Preliminary numerical results show that the proposed algorithm is very promising when compared with the tested SQP algorithms. 相似文献
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针对带不等式约束的极大极小问题,借鉴一般约束优化问题的模松弛强次可行SQP算法思想,提出了求解不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法.首先,通过在QCQP子问题中选取合适的罚函数,保证了算法的可行性以及目标函数F(x)的下降性,同时简化QCQP子问题二次约束项参数α_k的选取,可保证算法的可行性和收敛性.其次,算法步长的选取合理简单.最后,在适当的假设条件下证明了算法具有全局收敛性及强收敛性.初步的数值试验结果表明算法是可行有效的. 相似文献
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精确覆盖问题是组合优化中经典的NP-Hard问题之一,其在诸多领域具有广泛的应用价值。本文首先研究了精确覆盖问题的数学性质,并根据数学性质提出相应的分支降阶规则以缩小问题的规模;接着设计了一个基于分支降阶的回溯算法求解该问题;然后运用常规技术分析得出该精确算法的时间复杂度为O(1.4656k);最后运用加权分治技术对该算法的时间复杂度进行分析,将该算法的时间复杂度降为O(1.3842k)。文章最后通过一个示例进一步阐述该算法的原理,并与其他精确算法进行了对比分析,研究结果表明该算法是可行的,也是有效的。 相似文献
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Hong-gangXue Cheng-xianXu Feng-minXu 《计算数学(英文版)》2004,22(6):895-904
In this paper, we propose a new branch and bound algorithm for the solution of large scale separable concave programming problems. The largest distance bisection (LDB) technique is proposed to divide rectangle into sub-rectangles when one problem is branched into two subproblems. It is proved that the LDB method is a normal rectangle subdivision(NRS). Numerical tests on problems with dimensions from 100 to 10000 show that the proposed branch and bound algorithm is efficient for solving large scale separable concave programming problems, and convergence rate is faster than ω-subdivision method. 相似文献
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Julius ?ilinskas 《Journal of Global Optimization》2012,54(2):261-274
Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is minimization of a multimodal function with unfavorable properties like invariants and non-differentiability. Recently a branch and bound algorithm for multidimensional scaling with city-block distances has been proposed for solution of medium-size problems exactly. The algorithm exploits piecewise quadratic structure of the objective function. In this paper a parallel version of the branch and bound algorithm for multidimensional scaling with city-block distances has been proposed and investigated. Parallel computing enabled solution of larger problems what was not feasible with the sequential version. 相似文献
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为求线性比试和问题的全局最优解,本文给出了一个分支定界算法.通过一个等价问题和一个新的线性化松弛技巧,初始的非凸规划问题归结为一系列线性规划问题的求解.借助于这一系列线性规划问题的解,算法可收敛于初始非凸规划问题的最优解.算法的计算量主要是一些线性规划问题的求解.数值算例表明算法是切实可行的. 相似文献
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At the intersection of nonlinear and combinatorial optimization, quadratic programming has attracted significant interest
over the past several decades. A variety of relaxations for quadratically constrained quadratic programming (QCQP) can be
formulated as semidefinite programs (SDPs). The primary purpose of this paper is to present a systematic comparison of SDP
relaxations for QCQP. Using theoretical analysis, it is shown that the recently developed doubly nonnegative relaxation is
equivalent to the Shor relaxation, when the latter is enhanced with a partial first-order relaxation-linearization technique.
These two relaxations are shown to theoretically dominate six other SDP relaxations. A computational comparison reveals that
the two dominant relaxations require three orders of magnitude more computational time than the weaker relaxations, while
providing relaxation gaps averaging 3% as opposed to gaps of up to 19% for weaker relaxations, on 700 randomly generated problems
with up to 60 variables. An SDP relaxation derived from Lagrangian relaxation, after the addition of redundant nonlinear constraints
to the primal, achieves gaps averaging 13% in a few CPU seconds. 相似文献