共查询到19条相似文献,搜索用时 93 毫秒
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金照林 《数学的实践与认识》2023,(4):43-51
提出使用凸松弛的方法求解二层规划问题,通过对一般带有二次约束的二次规划问题的半定规划松弛的探讨,研究了使用半定规划(SDP)松弛结合传统的分枝定界法求解带有凸二次下层问题的二层二次规划问题,相比常用的线性松弛方法,半定规划松弛方法可快速缩小分枝节点的上下界间隙,从而比以往的分枝定界法能够更快地获得问题的全局最优解. 相似文献
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解带有二次约束二次规划的一个整体优化方法 总被引:1,自引:0,他引:1
在本文中,我们提出了一种解带有二次约束二次规划问题(QP)的新算法,这种方法是基于单纯形分枝定界技术,其中包括极小极大问题和线性规划问题作为子问题,利用拉格朗日松弛和投影次梯度方法来确定问题(QP)最优值的下界,在问题(QP)的可行域是n维的条件下,如果这个算法有限步后终止,得到的点必是问题(QP)的整体最优解;否则,该算法产生的点的序列{v^k}的每一个聚点也必是问题(QP)的整体最优解。 相似文献
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针对界约束二次规划的分枝定界法中出现的紧、松弛策略,结合聚类分析方法,给出了新的剖分边的选取原则,把球约束二次规划作为子问题,使得原问题整体最优值的上、下界能较快的达到. 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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本文针对一类带有反凸约束的非线性比式和分式规划问题,提出一种求其全局最优解的单纯形分支和对偶定界算法.该算法利用Lagrange对偶理论将其中关键的定界问题转化为一系列易于求解的线性规划问题.收敛性分析和数值算例均表明提出的算法是可行的. 相似文献
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本文提出了一个求不定二次规划问题全局最优解的新算法.首先,给出了三种计算下界的方法:线性逼近法、凸松弛法和拉格朗日松弛法;并且证明了拉格朗日对偶界与通过凸松弛得到的下界是相等的;然后建立了基于拉格朗日对偶界和矩形两分法的分枝定界算法,并给出了初步的数值试验结果. 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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Jaroslav M. Fowkes Nicholas I. M. Gould Chris L. Farmer 《Journal of Global Optimization》2013,56(4):1791-1815
We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. Unlike other branch and bound algorithms, lower bounds are obtained via nonconvex underestimators of the function. For a numerical example, we apply the proposed branch and bound algorithm to radial basis function approximations. 相似文献
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A global optimization method, QBB, for twice-differentiable NLPs (Non-Linear Programming) is developed to operate within a
branch-and-bound framework and require the construction of a relaxed convex problem on the basis of the quadratic lower bounding
functions for the generic nonconvex structures. Within an exhaustive simplicial division of the constrained region, the rigorous
quadratic underestimation function is constructed for the generic nonconvex function structure by virtue of the maximal eigenvalue
analysis of the interval Hessian matrix. Each valid lower bound of the NLP problem with the division progress is computed
by the convex programming of the relaxed optimization problem obtained by preserving the convex or linear terms, replacing
the concave term with linear convex envelope, underestimating the special terms and the generic terms by using their customized
tight convex lower bounding functions or the valid quadratic lower bounding functions, respectively. The standard convergence
properties of the QBB algorithm for nonconvex global optimization problems are guaranteed. The preliminary computation studies
are presented in order to evaluate the algorithmic efficiency of the proposed QBB approach. 相似文献
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Duality Bound Method for the General Quadratic Programming Problem with Quadratic Constraints 总被引:4,自引:0,他引:4
N. V. Thoai 《Journal of Optimization Theory and Applications》2000,107(2):331-354
The purpose of this article is to develop a branch-and-bound algorithm using duality bounds for the general quadratically-constrained quadratic programming problem and having the following properties: (i) duality bounds are computed by solving ordinary linear programs; (ii) they are at least as good as the lower bounds obtained by solving relaxed problems, in which each nonconvex function is replaced by its convex envelope; (iii) standard convergence properties of branch-and-bound algorithms for nonconvex global optimization problems are guaranteed. Numerical results of preliminary computational experiments for the case of one quadratic constraint are reported. 相似文献
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Many nonconvex nonlinear programming (NLP) problems of practical interest involve bilinear terms and linear constraints, as well as, potentially, other convex and nonconvex terms and constraints. In such cases, it may be possible to augment the formulation with additional linear constraints (a subset of Reformulation-Linearization Technique constraints) which do not affect the feasible region of the original NLP but tighten that of its convex relaxation to the extent that some bilinear terms may be dropped from the problem formulation. We present an efficient graph-theoretical algorithm for effecting such exact reformulations of large, sparse NLPs. The global solution of the reformulated problem using spatial Branch-and Bound algorithms is usually significantly faster than that of the original NLP. We illustrate this point by applying our algorithm to a set of pooling and blending global optimization problems. 相似文献
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We describe a general scheme for solving nonconvex optimization problems, where in each iteration the nonconvex feasible set
is approximated by an inner convex approximation. The latter is defined using an upper bound on the nonconvex constraint functions.
Under appropriate conditions, a monotone convergence to a KKT point is established. The scheme is applied to truss topology
design (TTD) problems, where the nonconvex constraints are associated with bounds on displacements and stresses. It is shown
that the approximate convex problem solved at each inner iteration can be cast as a conic quadratic programming problem, hence
large scale TTD problems can be efficiently solved by the proposed method. 相似文献
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A nonconvex generalized semi-infinite programming problem is considered, involving parametric max-functions in both the objective and the constraints. For a fixed vector of parameters, the values of these parametric max-functions are given as optimal values of convex quadratic programming problems. Assuming that for each parameter the parametric quadratic problems satisfy the strong duality relation, conditions are described ensuring the uniform boundedness of the optimal sets of the dual problems w.r.t. the parameter. Finally a branch-and-bound approach is suggested transforming the problem of finding an approximate global minimum of the original nonconvex optimization problem into the solution of a finite number of convex problems. 相似文献
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Linh T. H. Nguyen 《Optimization》2018,67(2):195-216
Motivated by weakly convex optimization and quadratic optimization problems, we first show that there is no duality gap between a difference of convex (DC) program over DC constraints and its associated dual problem. We then provide certificates of global optimality for a class of nonconvex optimization problems. As an application, we derive characterizations of robust solutions for uncertain general nonconvex quadratic optimization problems over nonconvex quadratic constraints. 相似文献