一个正定几何规划的对偶算法及收敛性

由于正定几何规划的对偶规划只含线性等式约束和非负约束,处理起来似乎要方便得多.然而,实际上许多对偶算法实施起来却往往失败(见[2,8,9]),这是由于对偶规划所特有的“块性质”以及目标函数在某些点的不可微性质引起的.因此,近年来主要的努力集中在克服这二个困难上。主要的工作有:1975年Beck和Ecker的修正凹单纯形     

LEVERRIER-LAGUERRE ALGORITHM FOR THE MATRIX POLYNOMIAL OF DEGREE TWO

1　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＡｂｅａｎ×ｎｍａｔｒｉｘ ,Ｉｎｄｅｎｏｔｅｓｔｈｅｕｎｉｔｍａｔｒｉｘｏｆｏｒｄｅｒｎ .Ａｎｄｌｅｔ ａ(λ) =ｄｅｔ(λＩｎ-Ａ) =λｎ+ ａ1λｎ- 1+… + ａｎ- 1λ+ ａｎ (1 .1 )ｂｅｔｈｅｃｈａｒａｃｔｅｒｉｓｔｉｃｐｏｌｙｎｏｍｉａｌｏｆＡ ,ｔｈｅａｄｊｏｉｎｔｍａｔｒｉｘｏｆλＩｎ-Ａｂｅ Ｂ(λ) =ａｄｊ(λＩｎ-Ａ) =λｎ- 1Ｉｎ+λｎ- 2 Ｂ1+… +λ Ｂｎ- 2 + Ｂｎ- 1. (1 .2 )Ｔｈｅｎ(λΙｎ-Ａ) - 1= Ｂ(λ) / ａ(λ) . (1 .3)　　Ａｗｅｌｌ ｋｎｏｗＬｅｖｅｒｒｉ…     

求首尾和r-循环矩阵的极小多项式的算法

研究了域上首尾和r-循环矩阵，利用多项式环的理想的Groebner基的算法给出了任意域上首尾和r-循环矩阵的极小多项式和公共极小多项式的一种算法.同时给出了这类矩阵逆矩阵的一种求法。     

二供应商经济批量问题的多项式时间算法

为了从采购费用结构不同的供应商中找到最佳补货策略,考虑一个零售商从两个供应商补货的二供应商经济批量问题.零售商在两个供应商处的采购费用结构分别为复合安装费用和全单位数量折扣费用结构.通过对问题结构性质的分析论证,将问题的可行解转化为一个有向网络,降低问题求解的计算复杂性.综合动态规划和Dijkstra最短路算法证明了该问题是多项式时间可解的.     

一类凸规划的多项式预估校正内点法

1、引言 1990年由Mehrotra对线性规划问题提出了一个称为预估校正的方法,并在1992年给出了其数值算法．1993年Mizuno,Todd和Y．Ye．给出了改进的预估校正内点法,使得一个预估步后只跟一个校正步．1994年F．A．Potra给出了不可行预估校正内点法,使得可以从一个不可行的初始点开始算法的迭代,并证明了其为二次收敛．     

AN ITERATIVE ALGORITHM FOR DETERMINING TIME－DEPENDENT COEFFICIENT OF TWO DIMENSIONAL LINEAR WAVE EQUATION

ＡＮＩＴＥＲＡＴＩＶＥＡＬＧＯＲＩＴＨＭＦＯＲＤＥＴＥＲＭＩＮＩＮＧＴＩＭＥ－ＤＥＰＥＮＤＥＮＴＣＯＥＦＦＩＣＩＥＮＴＯＦＴＷＯＤＩＭＥＮＳＩＯＮＡＬＬＩＮＥＡＲＷＡＶＥＥＱＵＡＴＩＯＮ（苏超伟）西北工业大学，邮编：７１００７２ＳｕＣｈａｏｗｅｉ（Ｎ...     

处理退化问题的一类SQP算法

本文对不等式优化问题提出了一个修正的序列二次规划算法(SQP).该算法适用于退化问题一积极约束梯度线性相关且严格互补条件不成立,并且算法是可行的,具有整体收敛与超线性收敛性.     

一类全局优化问题的区间斜率算法

考虑下面的全局优化问题: global minimize f(x),f:X~0 R~1→R~1 (1)其中X~0=[a~0,b~0],f是X~0上连续的多峰函数.在本文中f在X~0上的全局极小值记为f~*,f在X~0上所有全局极小点集合记为X~*.以下恒假定X~*仅由有限个点组成. 我们的目标是求f~*及X~*.求解这一问题已有诸多方法,这些方法一般可分为确定型和非确定型两类.前者以Lipschitz导数法,填充函数法等为代表,它们依据某一     

AN INTERVAL ALGORITHM FOR CONSTRAINED GLOBAL OPTIMIZATION

In order to solve the constrained global optimization problem,we use penalty functions not only on constraints but also on objective function. Then within the framework of interval analysis,an interval Branch-and-Bound algorithm is given,which does not need to solve a sequence of unconstrained problems. Global convergence is proved. Numerical examples show that this algorithm is efficient.     

A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING

This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O(n~(1/2)L) iteration complexity which is the best result for convex quadratic programming so far.     

稳定性判定与多项式求根算法

本文给出了一种判定多项式根是否全在单位圆内的简便方法．该方法可用于判定离散控制系统的稳定性和求多项式的全部根。     

一个约束乘积最大问题的强多项式时间算法

本文讨论了约束乘积最大问题最优解的结构特征,在此基础上给出了一个计算时间为O(n2)的强多项式时间算法,并且对于单边约束的情形给出了复杂度更低(O(nlnn))的强多项式时间算法.     

AN OUTER APPROXIMATION ALGORITHM FOR SEMI-INFINITE NONDIFFERENTIABLE PROGRAMMINGS

This paper presents a conceptual outer approximation algorithm for dealing with the semi-infinite nondifferentiable programming in which functions are locally Lipschitzian. By weakening the restriction on the family of functions for a parametric programming, we answer a question proposed in [1].     

单台机器成批加工最大延误问题的有效算法

在实际生产中,存在着大量成批加工的问题,即如何进行分批,以便使某一目标函数达到最优的问题。Ａｎｄｒｅｗｓ１９９５年的论文针对目标为最大延误的成批加工问题进行了分析和讨论,提出了一个寻找最优解的算法。虽然文章对一些特殊情况提出了减少计算量的措施,但文中的算法实质上仍然是基于枚举的指数算法。本文对该问题作了进一步的分析研究,发现了其内在的一些良好结构和性质,从而提出了一个求解它的多项式时间算法,计算量     

A SIMPLICIAL ALGORITHM FOR COMPUTING AN INTEGER ZERO POINT OF A MAPPING WITH THE DIRECTION PRESERVING PROPERTY

A mapping f:Z~n→R~n is said to possess the direction preserving property if fi(x)>0implies fi(y)≥0 for any integer points x and y with ‖x-y‖∞≤1.In this paper,a simplicial algorithm is developed for computing an integer zero point of a mappingwith the direction preserving property.We assume that there is an integer point x~0 withc≤x~0≤d satisfying that max_(1≤i≤n)(x_i-x_i~0)fi(x)>0 for any integer point x withf(x)≠0 on the boundary of H={x∈R~n|c-e≤x≤d e},where c and d are twofinite integer points with c≤d and e=(1,1,…1)~∈R~n.This assumption is impliedby one of two conditions for the existence of an integer zero point of a mapping with thepreserving property in van der Laan et al.(2004).Under this assumption, starting at x~0,the algorithm follows a finite simplicial path and terminates at an integer zero point ofthe mapping.This result has applications in general economic equilibrium models withindivisible commodities.     

一类广义分式规划问题的完全多项式时间近似算法

本文对一类广义分式规划问题,提出一种求其全局最优解的完全多项式时间近似算法,给出该算法的理论分析和计算复杂性,通过数值算例验证该算法是有效可行的.     

Clifford与Grassmann代数的理想的Groebner基

该文首先建立Clifford与Grassmann代数的理想的Groebner基的理论，给出该代数的理想的Groebner基的算法，从而解决了Clifford与 Grassmann代数的理想的成员问题.     

框式线性规划的多项式预估校正内点算法

本文研究带线性约束的框式线性规划问题,给出了一个预估校正内点算法,分析了该算法的多项式计算复杂性,并证明其迭代复杂度为Ο(nL).     

Multivariate Refinable Functions of High Approximation Order Via Quotient Ideals of Laurent Polynomials

We give an algebraic interpretation of the well-known zero-condition or sum rule for multivariate refinable functions with respect to an arbitrary scaling matrix. The main result is a characterization of these properties in terms of containment in a quotient ideal, however not in the ring of polynomials but in the ring of Laurent polynomials.