共查询到20条相似文献,搜索用时 62 毫秒
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对等式约束非线性规划问题的Hestenes-Powell增广拉格朗日函数的进一步研究 总被引:1,自引:0,他引:1
本文对用无约束极小化方法求解等式约束非线性规划问题的Hestenes-Powell 增广拉格朗日函数作了进一步研究.在适当的条件下,我们建立了Hestenes-Powell增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系,并且也给出了Hestenes-Powell增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系.因此,从理论的观点来看,原约束问题的解和对应的拉格朗日乘子值不仅可以用众所周知的乘子法求得,而且可以通过对Hestenes-Powell 增广拉格朗日函数在原问题变量和乘子变量的积空间上执行一个单一的无约束极小化来获得. 相似文献
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基于变换X=VV~T,本文将半定规划问题转换为非线性规划问题,提出了解决此问题的增广拉格朗日算法,并证明了算法的线性收敛性.在此算法中,每一次迭代计算的子问题利用最速下降搜索方向和满足wolf条件的线性搜索法求最优解.数值实验表明,此算法是行之有效的,且优于内点算法. 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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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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本文证明了带球(椭球)约束的不定二次规划问题具有强Lagrange对偶性,设计了一个求解这类问题的算法,本语文的结论比文「7」强,所设计的算法比文「7」简洁。 相似文献
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陈永林 《应用数学与计算数学学报》1993,7(1):1-13
本文提出了S-n.n.d.阵的概念,随之研究了相当一般的约束二次规划问题。本文还给出了S-n.n.d.阵A的基本加边矩阵的广义逆。§1.引言具有线性等式约束的二次规划问题(CQP)是最优化分支中最重要的问题之一。关于这个问题的理论方面与数值解法方面,已有许多文献。这个问题有许多形式,例如常见的形式是求函数 相似文献
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1.引言本文考虑如下边界约束的二次规划问题:其中QE*"""是对称的,C,人。E*"是给定的常数向量,且Z<。这类问题经常出现在偏微分方程,离散化的连续时间最优控制问题、线性约束的最小二乘问题、工程设计、或作为非线性规划方法中的序列子问题.因此具有特殊的重要性.本文提出求解问题(1.1)的分解方法.它类似求解线性代数方程组的选代法,它是对Q进行正则分裂【对即把Q分裂为两个矩阵之和,Q=N十片而这两个矩阵之差(N一则是对称正定的.在每次迭代中用一个易于求解的矩阵N替代Q进行计算一新的二次规划问题.在适… 相似文献
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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
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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
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A Global Optimization Method for Solving Convex Quadratic Bilevel Programming Problems 总被引:4,自引:0,他引:4
We use the merit function technique to formulate a linearly constrained bilevel convex quadratic problem as a convex program with an additional convex-d.c. constraint. To solve the latter problem we approximate it by convex programs with an additional convex-concave constraint using an adaptive simplicial subdivision. This approximation leads to a branch-and-bound algorithm for finding a global optimal solution to the bilevel convex quadratic problem. We illustrate our approach with an optimization problem over the equilibrium points of an n-person parametric noncooperative game. 相似文献
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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
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S. Cafieri M. D’Apuzzo M. Marino A. Mucherino G. Toraldo 《Journal of Optimization Theory and Applications》2006,129(1):55-75
In this paper, we present an interior-point algorithm for large and sparse convex quadratic programming problems with bound
constraints. The algorithm is based on the potential reduction method and the use of iterative techniques to solve the linear
system arising at each iteration. The global convergence properties of the potential reduction method are reassessed in order
to take into account the inexact solution of the inner system. We describe the iterative solver, based on the conjugate gradient
method with a limited-memory incomplete Cholesky factorization as preconditioner. Furthermore, we discuss some adaptive strategies
for the fill-in and accuracy requirements that we use in solving the linear systems in order to avoid unnecessary inner iterations
when the iterates are far from the solution. Finally, we present the results of numerical experiments carried out to verify
the effectiveness of the proposed strategies. We consider randomly generated sparse problems without a special structure.
Also, we compare the proposed algorithm with the MOSEK solver.
Research partially supported by the MIUR FIRB Project RBNE01WBBB “Large-Scale Nonlinear Optimization.” 相似文献
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Solving Standard Quadratic Optimization Problems via Linear, Semidefinite and Copositive Programming
The problem of minimizing a (non-convex) quadratic function over the simplex (the standard quadratic optimization problem) has an exact convex reformulation as a copositive programming problem. In this paper we show how to approximate the optimal solution by approximating the cone of copositive matrices via systems of linear inequalities, and, more refined, linear matrix inequalities (LMI's). In particular, we show that our approach leads to a polynomial-time approximation scheme for the standard quadratic optimzation problem. This is an improvement on the previous complexity result by Nesterov who showed that a 2/3-approximation is always possible. Numerical examples from various applications are provided to illustrate our approach. 相似文献
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本文提出一个新的解线性规划的Hopfields-型网络。该网络基于线性规划的对偶理论,并使用了Sigmoid函数,但不需要预先给定的罚参数和乘法模拟器,我们证明该网络不仅全局收敛到线性规划的精确解,而且能同时解原规划和对偶规划。由于在该网络中没有使用乘法模拟器而利用了Sigmoid函数,因此该模型是很容易用硬件实现的。 相似文献
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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