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1.
J. B. Jian 《Journal of Optimization Theory and Applications》2006,129(1):109-130
This paper discusses optimization problems with nonlinear inequality constraints and presents a new sequential quadratically-constrained
quadratic programming (NSQCQP) method of feasible directions for solving such problems. At each iteration. the NSQCQP method
solves only one subproblem which consists of a convex quadratic objective function, convex quadratic equality constraints,
as well as a perturbation variable and yields a feasible direction of descent (improved direction). The following results
on the NSQCQP are obtained: the subproblem solved at each iteration is feasible and solvable: the NSQCQP is globally convergent
under the Mangasarian-Fromovitz constraint qualification (MFCQ); the improved direction can avoid the Maratos effect without
the assumption of strict complementarity; the NSQCQP is superlinearly and quasiquadratically convergent under some weak assumptions
without thestrict complementarity assumption and the linear independence constraint qualification (LICQ).
Research supported by the National Natural Science Foundation of China Project 10261001 and Guangxi Science Foundation Projects
0236001 and 0249003.
The author thanks two anonymous referees for valuable comments and suggestions on the original version of this paper. 相似文献
2.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
We develop a convergence theory for convex and linearly constrained trust region methods which only requires that the step between iterates produce a sufficient reduction in the trust region subproblem. Global convergence is established for general convex constraints while the local analysis is for linearly constrained problems. The main local result establishes that if the sequence converges to a nondegenerate stationary point then the active constraints at the solution are identified in a finite number of iterations. As a consequence of the identification properties, we develop rate of convergence results by assuming that the step is a truncated Newton method. Our development is mainly geometrical; this approach allows the development of a convergence theory without any linear independence assumptions.Work supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38.Work supported in part by the National Science Foundation grant DMS-8803206 and by the Air Force Office of Scientific Research grant AFSOR-860080. 相似文献
10.
M. A. Diniz-Ehrhardt Z. Dostal M. A. Gomes-Ruggiero J. M. Martinez S. A. Santos 《Applications of Mathematics》2001,46(5):321-338
An algorithm for quadratic minimization with simple bounds is introduced, combining, as many well-known methods do, active set strategies and projection steps. The novelty is that here the criterion for acceptance of a projected trial point is weaker than the usual ones, which are based on monotone decrease of the objective function. It is proved that convergence follows as in the monotone case. Numerical experiments with bound-constrained quadratic problems from CUTE collection show that the modified method is in practice slightly more efficient than its monotone counterpart and has a performance superior to the well-known code LANCELOT for this class of problems. 相似文献
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12.
Z. Dostál A. Friedlander S.A. Santos K. Alesawi 《Computational Optimization and Applications》2002,23(1):127-133
In this paper we give corrections to our paper on an augmented Lagrangian type algorithm for strictly convex quadratic programming problems with equality constraints. 相似文献
13.
Jin-bao Jian Qing-jie Hu Chun-ming Tang Hai-yan Zheng 《Applied Mathematics and Optimization》2007,56(3):343-363
In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for
the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction
of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic
inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can
be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect,
an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved
to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported.
Project supported by the National Natural Science Foundation (No. 10261001), Guangxi Science Foundation (Nos. 0236001, 064001),
and Guangxi University Key Program for Science and Technology Research (No. 2005ZD02) of China. 相似文献
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Numerical test results are presented for solving smooth nonlinear programming problems with a large number of constraints, but a moderate number of variables. The active set method proceeds from a given bound for the maximum number of expected active constraints at an optimal solution, which must be less than the total number of constraints. A quadratic programming subproblem is generated with a reduced number of linear constraints from the so-called working set, which is internally changed from one iterate to the next. Only for active constraints, i.e., a certain subset of the working set, new gradient values must be computed. The line search is adapted to avoid too many active constraints which do not fit into the working set. The active set strategy is an extension of an algorithm described earlier by the author together with a rigorous convergence proof. Numerical results for some simple academic test problems show that nonlinear programs with up to 200,000,000 nonlinear constraints are efficiently solved on a standard PC. 相似文献
16.
Quasi-Newton methods in conjunction with the piecewise sequential quadratic programming are investigated for solving mathematical programming with equilibrium constraints, in particular for problems with complementarity constraints. Local convergence as well as superlinear convergence of these quasi-Newton methods can be established under suitable assumptions. In particular, several well-known quasi-Newton methods such as BFGS and DFP are proved to exhibit the local and superlinear convergence. 相似文献
17.
Mathematical Notes - 相似文献
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运用随机条件熵的概念和绝对平均收敛的一些性质,利用H S Chang研究齐次马氏链熵率收敛速度的方法考虑了在给定条件下的一类有限非齐次马氏链熵率的指数收敛速度. 相似文献
20.
A. Beck 《Journal of Optimization Theory and Applications》2009,142(1):1-29
We establish several convexity results which are concerned with nonconvex quadratic matrix (QM) functions: strong duality
of quadratic matrix programming problems, convexity of the image of mappings comprised of several QM functions and existence
of a corresponding S-lemma. As a consequence of our results, we prove that a class of quadratic problems involving several
functions with similar matrix terms has a zero duality gap. We present applications to robust optimization, to solution of
linear systems immune to implementation errors and to the problem of computing the Chebyshev center of an intersection of
balls.
This research was partially supported by the Israel Science Foundation under Grant ISF 489/06. 相似文献