共查询到18条相似文献,搜索用时 125 毫秒
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线性规划问题的可行域是一次线性不等式组,目标函数为一次线性函数,其内容覆盖了方程、不等式、集合运算、图象、坐标平移等基础知识,是一种很实用有效的数学方法,但因为其内容和方法简单,步骤程序化,所以近年高考题总是将其局限在选择题和填空题上,只是偶尔出现应用题,可以说命题正处于停滞不前状态.但是从线性规划问题的重要性来看,这是一个很好的命题资源,如何拓宽命题思路,改变程序化.使题目变得多姿多彩将是线性规划问题命题的方向.下面是几类常见的新题型. 相似文献
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线性规划是高中试验教材新增内容之一,解这类问题,通常都要先利用线性约束条件作出可行域,然后根据几何意义找到目标函数的最优解,但这种方法比较麻烦,既要画线,又要找点.比较费时.如果我们从线性约束条件入手,利用不等式的基本性质,将条件不等式进行等价变形与合理运算,往往会使问题迅速获解.下面。以近几年高考试题为例.予以说明. 相似文献
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本文对线性不等式约束的非线性规划问题提出了一类信赖域算法,证明了算法所产生的序列的任一聚点为Kuhn-Tucker点,并讨论了子问题求解的有效集方法. 相似文献
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《数学的实践与认识》2019,(24)
研究了一类二维非线性积分不等式组,该不等式组积分号外有非常数因子,不能用向量形式的Gronwall-Bellman型积分不等式进行估计.先利用Bernoulli不等式把非线性问题转化成线性问题,利用变量替换技巧和放大技巧研究只含有一个未知函数的积分不等式,接着利用两个引理和变量替换技巧和放大技巧给出不等式组中两个未知函数的估计.结果可用于研究积分、微分动力系统解的性质. 相似文献
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1 重难点分析本单元要求了解二元一次不等式表示的是直线一侧的平面区域 ,能够具体画出二元一次不等式(组 )所表示的平面区域 ,了解线性规划的意义及线性约束条件、线性目标函数、可行解、可行域、最优解等基本概念 ,了解线性规划问题的图解法 ,能用图解法求最优解及线性目标函数的最大值或最小值 ,能用线性规划的方法解决实际生活中简单的最优问题 ,培养提高对实际问题进行探索分析研究的能力 .本单元的重点是二元一次不等式表示的平面区域和解线性规划问题的图解法 .难点之一是确定二元一次不等式的解表示的是直线的哪一侧区域 ,解决此难… 相似文献
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本文研究了不等式约束的非线性规划问题.利用带滤子的无二次子规划(QP-free)非可行域方法,构造一个等价于原约束问题的一阶KKT条件的非光滑方程组,给出解这个方程组的迭代算法,并获得算法的全局收敛性. 相似文献
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As a synchronization parallel framework, the parallel variable transformation (PVT) algorithm is effective to solve unconstrained optimization problems. In this paper, based on the idea that a constrained optimization problem is equivalent to a differentiable unconstrained optimization problem by introducing the Fischer Function, we propose an asynchronous PVT algorithm for solving large-scale linearly constrained convex minimization problems. This new algorithm can terminate when some processor satisfies terminal condition without waiting for other processors. Meanwhile, it can enhances practical efficiency for large-scale optimization problem. Global convergence of the new algorithm is established under suitable assumptions. And in particular, the linear rate of convergence does not depend on the number of processors. 相似文献
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《Journal of Computational and Applied Mathematics》2002,145(1):133-149
The problem of finding an such that Ax⩽b and x⩾0 arises in numerous contexts. We propose a new optimization method for solving this feasibility problem. After converting Ax⩽b into a system of equations by introducing a slack variable for each of the linear inequalities, the method imposes an entropy function over both the original and the slack variables as the objective function. The resulting entropy optimization problem is convex and has an unconstrained convex dual. If the system is consistent and has an interior solution, then a closed-form formula converts the dual optimal solution to the primal optimal solution, which is a feasible solution for the original system of linear inequalities. An algorithm based on the Newton method is proposed for solving the unconstrained dual problem. The proposed algorithm enjoys the global convergence property with a quadratic rate of local convergence. However, if the system is inconsistent, the unconstrained dual is shown to be unbounded. Moreover, the same algorithm can detect possible inconsistency of the system. Our numerical examples reveal the insensitivity of the number of iterations to both the size of the problem and the distance between the initial solution and the feasible region. The performance of the proposed algorithm is compared to that of the surrogate constraint algorithm recently developed by Yang and Murty. Our comparison indicates that the proposed method is particularly suitable when the number of constraints is larger than that of the variables and the initial solution is not close to the feasible region. 相似文献
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This paper presents the convergence proof and complexity analysis of an interior-point framework that solves linear programming problems by dynamically selecting and adding relevant inequalities. First, we formulate a new primal–dual interior-point algorithm for solving linear programmes in non-standard form with equality and inequality constraints. The algorithm uses a primal–dual path-following predictor–corrector short-step interior-point method that starts with a reduced problem without any inequalities and selectively adds a given inequality only if it becomes active on the way to optimality. Second, we prove convergence of this algorithm to an optimal solution at which all inequalities are satisfied regardless of whether they have been added by the algorithm or not. We thus provide a theoretical foundation for similar schemes already used in practice. We also establish conditions under which the complexity of such algorithm is polynomial in the problem dimension and address remaining limitations without these conditions for possible further research. 相似文献
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The paper provides some examples of mutually dual unconstrained optimization problems originating from regularization problems for systems of linear equations and/or inequalities. The solution of each of these mutually dual problems can be found from the solution of the other problem by means of simple formulas. Since mutually dual problems have different dimensions, it is natural to solve the unconstrained optimization problem of the smaller dimension. 相似文献
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时贞军 《数学物理学报(A辑)》2004,4(6):675-682
该文提出一种无约束优化非线性共轭梯度法,证明了精确线性 搜索下的全局收敛性。当目标函数为一致凸函数时,证明了算法具有线性收敛速度。数值实验表明算法对于求解实际问题是有效的。 相似文献
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An Improved Method for Designing Quadrature Mirror Filter Banks via Unconstrained Optimization 总被引:1,自引:0,他引:1
This paper proposes an algorithm to design a two-channel linear phase quadrature mirror filter (QMF) bank. The design problem
is presented systematically as an unconstrained optimization that minimizes the weighted sum of error of transfer function
of the filter bank at quadrature frequency, stopband energy and the passband error of a prototype filter (PF). A new method
is developed for the design of a low pass prototype filter for QMF banks. For solving given optimization problem, Quasi-Newton
optimization technique is used. Numerical examples and comparisons with several existing methods are included to show the
performances and effectiveness of this method. An application of the proposed method is considered in the area of subband
coding of the images. 相似文献