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1.
利用Chen-Harker-Kanzow-Smale光滑技术,给出了一个求解箱约束二次规划的预估校正的算法,它是Xu‘s方程的进一步研究,它的思想是将问题的K-T条件转化成一组光滑的等式,再用预估校正方法求解.同现存的算法相比,该算法具有较快的收敛速度,且所需的条件相对较弱.本文改进了该领域内的一些最新结果. 相似文献
2.
The presence of complementarity constraints brings a combinatorial flavour to an optimization problem. A quadratic programming problem with complementarity constraints can be relaxed to give a semidefinite programming problem. The solution to this relaxation can be used to generate feasible solutions to the complementarity constraints. A quadratic programming problem is solved for each of these feasible solutions and the best resulting solution provides an estimate for the optimal solution to the quadratic program with complementarity constraints. Computational testing of such an approach is described for a problem arising in portfolio optimization.Research supported in part by the National Science Foundations VIGRE Program (Grant DMS-9983646).Research partially supported by NSF Grant number CCR-9901822. 相似文献
3.
A Non-Interior Path Following Method for Convex Quadratic Programming Problems with Bound Constraints 总被引:2,自引:1,他引:1
Song Xu 《Computational Optimization and Applications》2004,27(3):285-303
We propose a non-interior path following algorithm for convex quadratic programming problems with bound constraints based on Chen-Harker-Kanzow-Smale smoothing technique. Conditions are given under which the algorithm is globally convergent or globally linearly convergent. Preliminary numerical experiments indicate that the method is promising. 相似文献
4.
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
5.
Walter Murray 《Computational Optimization and Applications》1997,7(1):127-142
Sequential quadratic (SQP) programming methodsare the method of choice when solving small or medium-sized problems. Sincethey are complex methods they are difficult (but not impossible) to adapt tosolve large-scale problems. We start by discussing the difficulties that needto be addressed and then describe some general ideas that may be used toresolve these difficulties. A number of SQP codes have been written to solve specific applications and there is a general purposed SQP code called SNOPT,which is intended for general applications of a particular type. These aredescribed briefly together with the ideas on which they are based. Finally wediscuss new work on developing SQP methods using explicit second derivatives. 相似文献
6.
针对共轭梯度法求解无约束二次凸规划时,在构造共轭方向上的局限性,对共轭梯度法进行了改进.给出了构造共轭方向的新方法,利用数学归纳法对新方法进行了证明.同时还给出了改进共轭梯度法在应用时的基本计算过程,并对方法的收敛性进行了证明.通过实例求解,说明了在求解二次无约束凸规划时,该方法相比共轭梯度法具有一定的优势. 相似文献
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9.
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
10.
Yong Zhang Ting‐Zhu Huang Yan‐Fei Jing Liang Li 《Numerical Linear Algebra with Applications》2012,19(3):555-569
An incomplete Cholesky (IC) factorization with multi‐parameters is presented. The marked virtue of the proposed IC factorization algorithm is to dynamically control the number of nonzero elements in each column of the IC factorization preconditioner L with the help of these involved parameters. Parameter setting strategies are also given. Numerical results show that the total computing time for both computation of the preconditioner L and iterative solution is evidently reduced for almost all test matrices. In general, these parameters can obviously enhance the effectiveness and performance of the IC factorization. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
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
12.
A class of new affine-scaling interior-point Newton-type methods are considered for the solution of optimization problems
with bound constraints. The methods are shown to be locally quadratically convergent under the strong second order sufficiency
condition without assuming strict complementarity of the solution. The new methods differ from previous ones by Coleman and
Li [Mathematical Programming, 67 (1994), pp. 189–224] and Heinkenschloss, Ulbrich, and Ulbrich [Mathematical Programming, 86 (1999), pp. 615–635] mainly in the choice of the scaling matrix. The scaling matrices used here have stronger smoothness
properties and allow the application of standard results from non smooth analysis in order to obtain a relatively short and
elegant local convergence result. An important tool for the definition of the new scaling matrices is the correct identification
of the degenerate indices. Some illustrative numerical results with a comparison of the different scaling techniques are also
included. 相似文献
13.
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
14.
In this paper we introduce an augmented Lagrangian type algorithm for strictly convex quadratic programming problems with equality constraints. The new feature of the proposed algorithm is the adaptive precision control of the solution of auxiliary problems in the inner loop of the basic algorithm. Global convergence and boundedness of the penalty parameter are proved and an error estimate is given that does not have any term that accounts for the inexact solution of the auxiliary problems. Numerical experiments illustrate efficiency of the algorithm presented 相似文献
15.
Durazzi C. Ruggiero V. Zanghirati G. 《Journal of Optimization Theory and Applications》2001,110(2):289-313
This paper concerns the use of iterative solvers in interior-point methods for linear and quadratic programming problems. We state an adaptive termination rule for the inner iterative scheme and we prove the global convergence of the obtained algorithm, exploiting the theory developed for inexact Newton methods. This approach is promising for problems with special structure on parallel computers. We present an application on Cray T3E/256 and SGI Origin 2000/64 arising in stochastic linear programming and robust optimization, where the constraint matrix is block-angular and extremely large. 相似文献
16.
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
17.
Using a Mixed Integer Quadratic Programming Solver for the Unconstrained Quadratic 0-1 Problem 总被引:1,自引:0,他引:1
In this paper, we consider problem (P) of minimizing a quadratic function q(x)=x
t
Qx+c
t
x of binary variables. Our main idea is to use the recent Mixed Integer Quadratic Programming (MIQP) solvers. But, for this,
we have to first convexify the objective function q(x). A classical trick is to raise up the diagonal entries of Q by a vector u until (Q+diag(u)) is positive semidefinite. Then, using the fact that x
i
2=x
i, we can obtain an equivalent convex objective function, which can then be handled by an MIQP solver. Hence, computing a suitable
vector u constitutes a preprocessing phase in this exact solution method. We devise two different preprocessing methods. The first
one is straightforward and consists in computing the smallest eigenvalue of Q. In the second method, vector u is obtained once a classical SDP relaxation of (P) is solved.
We carry out computational tests using the generator of (Pardalos and Rodgers, 1990) and we compare our two solution methods
to several other exact solution methods. Furthermore, we report computational results for the max-cut problem. 相似文献
18.
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
19.
Described here is the structure and theory for a sequential quadratic programming algorithm for solving sparse nonlinear optimization problems. Also provided are the details of a computer implementation of the algorithm along with test results. The algorithm maintains a sparse approximation to the Cholesky factor of the Hessian of the Lagrangian. The solution to the quadratic program generated at each step is obtained by solving a dual quadratic program using a projected conjugate gradient algorithm. An updating procedure is employed that does not destroy sparsity. 相似文献