共查询到20条相似文献,搜索用时 46 毫秒
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The so called dual parameterization method for quadratic semi-infinite programming (SIP) problems is developed recently. A dual parameterization algorithm is also proposed for numerical solution of such problems. In this paper, we present and improved adaptive algorithm for quadratic SIP problems with positive definite objective and multiple linear infinite constraints. In each iteration of the new algorithm, only a quadratic programming problem with a limited dimension and a limited number of constraints is required to be solved. Furthermore, convergence result is given. The efficiency of the new algorithm is shown by solving a number of numerical examples. 相似文献
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The so called dual parametrization method for quadratic semi-infinite programming (SIP) problems is developed recently for quadratic SIP problems with a single infinite constraint. A dual parametrization algorithm is also proposed for numerical solution of such problems. In this paper, we consider quadratic SIP problems with positive definite objective and multiple linear infinite constraints. All the infinite constraints are supposed to be continuously dependent on their index variable on a compact set which is defined by a number equality and inequalities. We prove that in the multiple infinite constraint case, the minimu parametrization number, just as in the single infinite constraint case, is less or equal to the dimension of the SIP problem. Furthermore, we propose an adaptive dual parametrization algorithm with convergence result. Compared with the previous dual parametrization algorithm, the adaptive algorithm solves subproblems with much smaller number of constraints. The efficiency of the new algorithm is shown by solving a number of numerical examples. 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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F. Güder 《The Journal of the Operational Research Society》1988,39(12):1147-1154
This paper describes a partitioning algorithm based on the Benders decomposition to solve net import spatial equilibrium models. The method decomposes the problem into a linear master problem and a quadratic subproblem. It is shown that the quadratic subproblem is trivial, and the associated dual variables can be determined through ordinary calculus. Therefore, the quadratic spatial equilibrium problem is solved iteratively by using linear programming software. 相似文献
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Stabilized Sequential Quadratic Programming 总被引:2,自引:0,他引:2
William W. Hager 《Computational Optimization and Applications》1999,12(1-3):253-273
Recently, Wright proposed a stabilized sequential quadratic programming algorithm for inequality constrained optimization. Assuming the Mangasarian-Fromovitz constraint qualification and the existence of a strictly positive multiplier (but possibly dependent constraint gradients), he proved a local quadratic convergence result. In this paper, we establish quadratic convergence in cases where both strict complementarity and the Mangasarian-Fromovitz constraint qualification do not hold. The constraints on the stabilization parameter are relaxed, and linear convergence is demonstrated when the parameter is kept fixed. We show that the analysis of this method can be carried out using recent results for the stability of variational problems. 相似文献
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对框式凸二次规划问题提出了一种非精确不可行内点算法 ,该算法使用的迭代方向仅需要达到一个相对的精度 .在初始点位于中心线的某邻域内的假设下 ,证明了算法的全局收敛性 相似文献
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A Method for Solving Certain Quadratic Programming Problems Arising in Nonsmooth Optimization 总被引:2,自引:0,他引:2
We present a finite algorithm for minimizing a piecewise linearconvex function augmented with a simple quadratic term. To solvethe dual problem, which is of least-squares form with an additionallinear term, we include in a standard active-set quadratic programmingalgorithm a new column-exchange strategy for treating positivesemidefinite problems. Numerical results are given for an implementationusing the Cholesky factorization. 相似文献
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A Proportioning Based Algorithm with Rate of Convergence for Bound Constrained Quadratic Programming
Z. Dostál 《Numerical Algorithms》2003,34(2-4):293-302
The proportioning algorithm with projections turned out to be an efficient algorithm for iterative solution of large quadratic programming problems with simple bounds and box constraints. Important features of this active set based algorithm are the adaptive precision control in the solution of auxiliary linear problems and capability to add or remove many indices from the active set in one step. In this paper a modification of the algorithm is presented that enables to find its rate of convergence in terms of the spectral condition number of the Hessian matrix and avoid any backtracking. The modified algorithm is shown to preserve the finite termination property of the original algorithm for problems that are not dual degenerate. 相似文献
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Efficient Sequential Quadratic Programming Implementations for Equality-Constrained Discrete-Time Optimal Control 总被引:1,自引:0,他引:1
Efficient sequential quadratic programming (SQP) implementations are presented for equality-constrained, discrete-time, optimal control problems. The algorithm developed calculates the search direction for the equality-based variant of SQP and is applicable to problems with either fixed or free final time. Problem solutions are obtained by solving iteratively a series of constrained quadratic programs. The number of mathematical operations required for each iteration is proportional to the number of discrete times N. This is contrasted by conventional methods in which this number is proportional to N
3. The algorithm results in quadratic convergence of the iterates under the same conditions as those for SQP and simplifies to an existing dynamic programming approach when there are no constraints and the final time is fixed. A simple test problem and two application problems are presented. The application examples include a satellite dynamics problem and a set of brachistochrone problems involving viscous friction. 相似文献
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An augmented Lagrangian nonlinear programming algorithm has been developed. Its goals are to achieve robust global convergence and fast local convergence. Several unique strategies help the algorithm achieve these dual goals. The algorithm consists of three nested loops. The outer loop estimates the Kuhn-Tucker multipliers at a rapid linear rate of convergence. The middle loop minimizes the augmented Lagrangian functions for fixed multipliers. This loop uses the sequential quadratic programming technique with a box trust region stepsize restriction. The inner loop solves a single quadratic program. Slack variables and a constrained form of the fixed-multiplier middleloop problem work together with curved line searches in the inner-loop problem to allow large penalty wieghts for rapid outer-loop convergence. The inner-loop quadratic programs include quadratic onstraint terms, which complicate the inner loop, but speed the middle-loop progress when the constraint curvature is large.The new algorithm compares favorably with a commercial sequential quadratic programming algorithm on five low-order test problems. Its convergence is more robust, and its speed is not much slower.This research was supported in part by the National Aeronautics and Space Administration under Grant No. NAG-1-1009. 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
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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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一种内点法解二次规划 总被引:2,自引:0,他引:2
二次规划(QP)为NP完全问题,本文研究了一种简单形式的二次规划。 一种基于依赖域子问题和内点法的算法被给出,其全局收敛被给出,特殊情况下,具有局部二次收敛。 相似文献
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二次分配问题(Quadratic assignment problem,QAP)属于NP-hard组合优化难题.二次分配问题的线性化及下界计算方法,是求解二次分配问题的重要途径.以Frieze-Yadegar线性化模型和Gilmore-Lawler下界为基础,详细论述了二次分配问题线性化模型的结构特征,并分析了Gilmore-Lawler下界值往往远离目标函数最优值的原因.在此基础上,提出一种基于匈牙利算法的二次分配问题对偶上升下界求解法.通过求解QAPLIB中的部分实例,说明了方法的有效和可行性. 相似文献
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Extended Linear-Quadratic Programming (ELQP) problems were introduced by Rockafellar and Wets for various models in stochastic programming and multistage optimization. Several numerical methods with linear convergence rates have been developed for solving fully quadratic ELQP problems, where the primal and dual coefficient matrices are positive definite. We present a two-stage sequential quadratic programming (SQP) method for solving ELQP problems arising in stochastic programming. The first stage algorithm realizes global convergence and the second stage algorithm realizes superlinear local convergence under a condition calledB-regularity.B-regularity is milder than the fully quadratic condition; the primal coefficient matrix need not be positive definite. Numerical tests are given to demonstrate the efficiency of the algorithm. Solution properties of the ELQP problem underB-regularity are also discussed.Supported by the Australian Research Council. 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