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In this paper, we propose a parametric approach to the stability theory for the solution set of a semiinfinite linear inequality system in the ndimensional Euclidean space


A linear inequality system with infinitely many constraints is polynomial [analytical] if its index set is a compact interval of the real line and all its coefficients are polynomial [analytical] functions of the index on this interval.


We consider the error bounds for a piecewise affine inequality system and present a necessary and sufficient condition for this system to have an error bound, which generalizes the Hoffman result.


We consider a given closed convex set represented by a certain linear inequality system σ whose coefficients can be arbitrarily perturbed, and we measure the size of these perturbations by means of the pseudometric of the uniform convergence.


The mixed cells are reformulated in terms of a linear inequality system with an additional combinatorial condition.

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 Using PseudoBoolean method as Optimization algorithm is especially Suitable for solving optimization problems with bivalent variables. In this paper, the writer proposes a method known as linear PseudoBoolean inequality system programming for solving the optimization of coefficient words length of IIR digital filters. The basic principleand solving procedure are introduced, the effectiveness of this method was proved with examples of optimization of coefficient words length of 6th order lowpass and 8th... Using PseudoBoolean method as Optimization algorithm is especially Suitable for solving optimization problems with bivalent variables. In this paper, the writer proposes a method known as linear PseudoBoolean inequality system programming for solving the optimization of coefficient words length of IIR digital filters. The basic principleand solving procedure are introduced, the effectiveness of this method was proved with examples of optimization of coefficient words length of 6th order lowpass and 8th order bandpass elliptic digital filters.  作为一种优化算法,利用伪布尔函数特别适用于解决其变量可以表示成0,1二个数字的优化问题。本文首次提出将“解线性伪布尔不等式系统”的算法应用于IIR数字滤波器系数字长的优化问题。文章介绍了算法的基本原理并用一个6阶低通滤波器及一个8阶带通滤波器对本算法的有效性进行了验证。  This paper presents a family of iterative method with fixed objective valuesfor solving the inequality system of nonlinear functionsa_i≤f_i(x)≤b_i (i(?)I_1~*)a_i≤f_i(x) (i(?)I_2~*)and discusses its application to automatic lens design.Each iterative method in the above mentioned family possesses the followingtwo important automatically adjustive properties:1.If f_i(x~(k))∈(f_i~*αki ε_i,f_i~*+αki ε_i)(?)(a_i,b_i),then f_i(x~(k+i))∈(a_i,b_i),wheref_i~*=2~(1)(a_i+b_i),ε_i=2~(1)(b_ia_i),b_i>a_i(i∈ j_2~*),αki∈(0,1],I=1,2,…,i(?)I=I_1~*... This paper presents a family of iterative method with fixed objective valuesfor solving the inequality system of nonlinear functionsa_i≤f_i(x)≤b_i (i(?)I_1~*)a_i≤f_i(x) (i(?)I_2~*)and discusses its application to automatic lens design.Each iterative method in the above mentioned family possesses the followingtwo important automatically adjustive properties:1.If f_i(x~(k))∈(f_i~*αki ε_i,f_i~*+αki ε_i)(?)(a_i,b_i),then f_i(x~(k+i))∈(a_i,b_i),wheref_i~*=2~(1)(a_i+b_i),ε_i=2~(1)(b_ia_i),b_i>a_i(i∈ j_2~*),αki∈(0,1],I=1,2,…,i(?)I=I_1~* U I_2~*,andx~(k)(k=0,1,2,…)being iterative points.2.Each system {f_i(x~(k+1))i(?)I}at each iterative point=x~(k+1)(k=0,1,2…)can automatically be adjusted by some given rules.  本文提供一个解非线性不等式组(1.1)的固定目标值迭代方法族.这个族中的每个迭代方法不但能使在迭代点的函数值收敛到锁向精度后不再超出精度区间和使未收敛到锁向精度的函数有较快的速度向精变区间收敛.而且还有多种自动调节功能.  The mathematical formula in similarity of linear equality or linear inequality system with degeneration is finally obtained when many structural optimization problems are solved with optimality criterion method, as well as general mathematical programming. In this case, many algorithms fail to get solution or perform poorly. A unified method presented in this paper which is based on method presented in thispaper which is based on simplex method of linear propramming in used to overcome the difficulty mentioned... The mathematical formula in similarity of linear equality or linear inequality system with degeneration is finally obtained when many structural optimization problems are solved with optimality criterion method, as well as general mathematical programming. In this case, many algorithms fail to get solution or perform poorly. A unified method presented in this paper which is based on method presented in thispaper which is based on simplex method of linear propramming in used to overcome the difficulty mentioned previously. Optimality criterion method, constrained second order approximation method, NewtonRaphson method, the secone order algorithms of the Fleury's dual method and other method have been improved by using the basic idea of the method discussed in this paper, Numerical examples are given showing the validity of the method.  在结构优化准则法中,乃至一般的数学规划问题中,存在大量问题有相近的数学形式,通常是具有退化性质的线性等式或不等式系统,各种具体的解法往往失效,本文提出一个基于线性规划单纯形法之上的统一方法解决了这一困难。无论对于准则法,约束二阶近似的方法,NewtonRaphson方法,Fleury的对偶方法的二阶算法,本文提出的方法都是有效的,数值例子支持了该方法。   << 更多相关文摘 
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