一类大规模二次规划问题的可行下降分解算法

本文对一类大规模二次规划问题，提出了矩阵剖分的概念和方法，并将问题转化为求解一系列容易求解的小规模二次规划子问题．另外，通过施加某些约束机制，使子问题所产生的迭代点均为可行下降点．在通常的假定下，证明算法具有全局收敛性，大量数值实验表明，本文所提出的新算法是有效的。     

The Minimum Number of Basic Feasible Solutions to a Transport Problem

In this paper, combinatorial arguments are used to derive a lower bound to the number of basic feasible solutions of a transport problem. A separate argument is given for degenerate and non-degenerate systems, and an example which attains the lower bound is given for each type.     

求基可行解一种概率意义下的多项式算法

本文对求线性规划问题的基可行解，给出一种改型算法，证明它对m个约束、n个变量的问题，当n≥2m时，为使求得一个基可行解的概率大于0．98，对m>24，所需迭代次数不超过（m＋3），而对m≥76，迭代次数已不超过（m＋1）．     

Feasible direction method for large-scale nonconvex programs: Decomposition approach

In this paper, we propose a feasible-direction method for large-scale nonconvex programs, where the gradient projection on a linear subspace defined by the active constraints of the original problem is determined by dual decomposition. Results are extended for dynamical problems which include distributed delays and constraints both in state and control variables. The approach is compared with other feasible-direction approaches, and the method is applied to a power generation problem. Some computational results are included.This work was supported by the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, Brasilia, Brasil, and by the Fundaçao de Amparo a Pesquisa do Estado de Sao Paulo, Sao Paulo, Brazil.On leave from UNICAMP, Campinas, Brazil.     

线性规划求基可行解的一种方法

本文通过增加一个特殊约束,贯彻对偶单纯形法检验数全非正的思想,迭代求优;然后再去掉该约束,结果却可得到一个基可行解。上述过程经简化处理后,增减约束可以不必出现,它仅使单纯形表矩阵增加几次初等变换而已,足见其方法之简捷及有效性。     

多目标交互可行方向法

对于多目标非线性规划问题，本文借助修正Zoutendijk法的可行方向思想，利用ε－约束问题的K－T乘子和决策者提供的权衡比产生变形标量化问题的可行下降方向，逐步求得决策者满意的有效解．     

An Algorithm for the Modular Decomposition of Hypergraphs

We propose an O(n⁴) algorithm to build the modular decomposition tree of hypergraphs of dimension three and show how this algorithm can be generalized to compute in O(n^{3k − 5}) time the decomposition of hypergraphs of any fixed dimension k.     

基于区域分解的CRS算法

本文针对带有盒子约束的非线性规划问题提出一种算法,该算法把解空间分成几个区域,根据每个区域上解的信息定义其选择概率,再根据轮盘赌选择法选择某个区域,在选择的区域上进行CRS（Control Random Search）算法操作。该方法能够缩小搜索空间,从而提高算法的搜索能力及算法的收敛速度,特别是在算法的后期效果更加明显。最后把提出的算法应用到两个典型的函数优化问题中,数值结果表明,算法是可行的、有效的。     

一个矩阵分解算法的推广及应用

对样本相关系数矩阵等行和分解算法作了简化和推广,使算法不仅可以应用在基于正态总体非独立样本的假设检验问题,也可以有效地运用在最优化算法中牛顿法等与二次函数极小化有关的问题上.     

线性规划问题退化最优基可行解的性质

本通过分析两用阶段法求解线性规划初始可行解的一个例子,归纳了线性规划问题退化的最优基可行解的性质,包括同一退化最优基可行解不同表示,有无穷多最优解的表示。     

关于群表示的分解矩阵和Cartan矩阵的两个结论

讨论了群表示中关于Cartan矩阵,Brauer特征等的性质,得到了一些结论,由这些结论,引进了所谓高度的一类概念,利用这一类概念证明了群表示论中关于分解矩阵和Cartan矩阵的两个结论.     

多目标非线性规划的可行方向交互算法

本文提出一个求解多目标非线性规划问题的交互规划算法．在每一轮迭代中,此法仅要求决策者提供目标间权衡比的局部信息．算法中的可行方向是基于求解非线性规划问题的Topkis－Veinott法构千的．我们证明,在一定条件下,此算法收敛于问题的有效解．     

A New Successive Partition Algorithm for Concave Minimization Based on Cone Decomposition and Decomposition Cuts

In this paper we propose a new partition algorithm for concave minimization. The basic structure of the algorithm resembles that of conical algorithms. However, we make extensive use of the cone decomposition concept and derive decomposition cuts instead of concavity cuts to perform the bounding operation. Decomposition cuts were introduced in the context of pure cutting plane algorithms for concave minimization and has been shown to be superior to concavity cuts in numerical experiments. Thus by using decomposition cuts instead of concavity cuts to perform the bounding operation, unpromising parts of the feasible region can be excluded from further explorations at an earlier stage. The proposed successive partition algorithm finds an -global optimal solution in a finite number of iterations.     

不等式约束优化一个超线性收敛的可行内点型算法

本文针对非线性不等式约束优化问题,提出了-个可行内点型算法.在每次迭代中,基于积极约束集策略,该算法只需求解三个线性方程组,因而其计算工作量较小.在-般的条件下,证明了算法具有全局收敛及超线性收敛性.     

A variable dimension algorithm with the Dantzig-Wolfe decomposition for structured stationary point problems

Given a set ofR ⁿ and a functionf from intoR ⁿ we consider a problem of finding a pointx ^* in such that(x–x ^*) ^t f(x ^*)0 holds for every pointx in. This problem is called the stationary point problem and the pointx ^* is called a stationary point. We present a variable dimension algorithm for solving the stationary point problem with an affine functionf on a polytope defined by constraints of linear equations and inequalities. We propose a system of equations whose solution set contains a piecewise linear path connecting a trivial starting point in with a stationary point. The path can be followed by solving a series of linear programs which inherit the structure of constraints of. The linear programs are solved efficiently with the Dantzig-Wolfe decomposition method by exploiting fully the structure.Part of this research was carried out when the first author was supported by the Center for Economic Research, Tilburg University, The Netherlands and the third author was supported by the Alexander von Humboldt-Foundation, Federal Republic of Germany.     

Feasible Direction Algorithm for Optimal Control Problems with State and Control Constraints: Implementation

In this paper, we describe the implementation aspects of an optimization algorithm for optimal control problems with control, state, and terminal constraints presented in our earlier paper. The important aspect of the implementation is that, in the direction-finding subproblems, it is necessary only to impose the state constraint at relatively few points in the time involved. This contributes significantly to the algorithmic efficiency. The algorithm is applied to solve several optimal control problems, including the problem of the abort landing of an aircraft in the presence of windshear.     

Uniform Asymptotic Representation of Solutions of the Basic Semiconductor-Device Equations

In this paper we analyse the basic semiconductor-device equationsmodelling a symmetric one-dimensional voltage-controlled diodeunder the assumptions of zero recombination-generation and constantmobilities. Employing the singular-perturbation formulationwith the normed Debye length as perturbation parameter we derivethe zeroth-order terms of the matched asymptotic expansion ofthe solutions, which are sums of uniformly smooth outer terms(reduced solutions) and exponentially varying inner terms (layersolutions). The main result of the paper is that, if the perturbationparameter is sufficiently small, then there exists a solutionof the semiconductor-device problem which is approximated uniformlyby the zeroth-order term of the expansion, even for large appliedvoltages. This result shows the validity of the asymptotic expansionsof the solutions of the semiconductor-device problem in physicallyrelevant high-injection situations.     

不等式约束最优化的一个使用非单调搜索的可行算法

对不等式约束最优化问题本文提出了一个新算法。算法使用了非单调搜索,它不仅放松了每步迭代中对搜索的限制,而且使得算法迭代到一定阶段后具有非常简洁的形式,在不需要严格互补条件的较弱假设下,算法是整体和超线性收敛的。