有界变量线性规划的基线算法

本文对有界变量线性规划的算法进行了研究，得到了一种解此问题的新算法。文中根据基线算法的算法原理，通过对BL表的旋转，在各变量满足界约束的条件下，使目标函数值不断增大，直至得到有界硬上界，从而得到问题的最优解。文中给出了有界变量线性规划基线算法的计算步骤，并给出了一个例子。与单纯形法相比，采用基线算法解有界变量线性规划操作更简单。迭代次数少，解题速度更快。     

线性方程组的多维投影算法

本文分析了求解线性方程组的一维投影算法即最小剩余法。定义了长轴陷阱及陷阱深度，用它们刻划了该算法迭代过程中锯齿现象的几何特征。本文给出了基于残差序列的避开长轴陷阱的扰动技巧，即多维投影算法。数值试验表明，投影算法要优于现在流行的主要算法。     

求解一类约束优化问题的Newton分裂算法

本文给出了求解一类约束优化问题的一个Newton分裂算法，并证明了算法的局部平方收敛性，该算法与已有算法相比，具有计算量小的特点，因而特别适合于求解大规模问题，为进一步降低算法的计算复杂性，我们结合Broyden算法，给出了两类Broyden类分裂算法。     

求解不等式约束优化问题的一个改进算法

本文改进了一个求解不等式约束优化问题的对偶算法，建立了一个相应的算法，进一步证明了该算法的收敛性．最后，给出数值结果以验证该算法的有效性。     

两台机器超载实时系统的On-line算法

对超载实时系统的On—line算法中的SR算法作了修改，提出了NSR算法，并证明NSR算法的竞争比至少为2／5，因而它比SR算法更为优异．     

对一类overlay层组播路由问题的模型的改进

根据overlay层虚拟网图的特点，本给出了一类overlay层组播路由问题的数学模型的改进，及相应的一种启发式算法，即MMD算法，并分析了该算法的性质，证明了它是一个多项式时间算法。     

一类教育最优投资模型的快速瓶颈消除算法

本提出了一类教育最优投资模型的快速瓶颈消除算法，给出了算法的思想和具体迭代过程，对算法的最优性进行了证明。最后通过实例给出了算法直观的表上作业法。该算法迭代次数非常少，是一种实用的好算法。     

算法教学中丰富的数学思想

掌握算法和算法思想是信息时代对学生提出的一项新要求，算法进入中学数学课程也是世界课程改革的一大潮流．我国高中数学新课程就顺应了这种趋势，第一次把算法引入高中数学课程．新课标中提出：“学生要通过对具体问题过程与步骤的分析，体会算法思想，了解算法的含义．”在教学说明意见部分提出，要将算法思想渗透到高中课程的其他相关内容．从广义上讲，每一个问题（特别是数学问题）的解决都对应着一个算法，研究问题的方法就是研究算法．而算法思想，应该包括两个层面：     

一种基于核心矩阵的原始对偶算法

本文通过对线性规划问题中的核心矩阵的分析，提出了一种基于核心矩阵的原始对偶算法。该算法以核心矩阵为运算单元，一方面呈现了存储空间小，计算量小的特点；另一方面，该算法采用了一种新的转轴规则的外点算法，在保持原始可行的基础上，不断改善对偶解使其可行。数值实验结果表明该算法在迭代次数、转轴效率和存储空间上都有一定的提高。     

线性互补问题的阻尼牛顿法的有限终止性

在（２）中，Ｈａｒｋｅｒ和Ｐａｎｇ提出了如下一个公开问题，对于线性互补问题的阻尼牛顿算法，当它收敛时，算法是否能在有限步内终止？本文对此问题给出一个肯定回答，而且进一步给出一个新的求解一般线性互补问题的有限终止算法，这个算法避免了阻尼牛顿算法可能不收敛的情形。     

A fraction free Matrix Berlekamp/Massey algorithm

We describe a fraction free version of the Matrix Berlekamp/Massey algorithm. The algorithm computes a minimal matrix generator of linearly generated square matrix sequences in an integral domain. The algorithm performs all operations in the integral domain, so all divisions performed are exact. For scalar sequences, the matrix algorithm specializes to a different algorithm than the algorithm currently in the literature. This new scalar algorithm has smaller intermediate values than the known fraction free Berlekamp/Massey algorithm.     

A descent algorithm for nonsmooth convex optimization

This paper presents a new descent algorithm for minimizing a convex function which is not necessarily differentiable. The algorithm can be implemented and may be considered a modification of the ε-subgradient algorithm and Lemarechal's descent algorithm. Also our algorithm is seen to be closely related to the proximal point algorithm applied to convex minimization problems. A convergence theorem for the algorithm is established under the assumption that the objective function is bounded from below. Limited computational experience with the algorithm is also reported.     

一种新的双模式盲均衡算法研究

针对恒模算法(CMA)收敛速度较慢、收敛后均方误差较大的缺点,提出一种新的双模式盲均衡算法.在算法初期,利用能快速收敛的归一化恒模算法(NCMA)进行冷启动,在算法收敛后切换到判决引导(DD-LMS)算法,减少误码率.计算机仿真表明,提出的新算法有较快的收敛速度和较低的误码率.     

A rank-one algorithm for unconstrained function minimization

A rank-one algorithm is presented for unconstrained function minimization. The algorithm is a modified version of Davidon's variance algorithm and incorporates a limited line search. It is shown that the algorithm is a descent algorithm; for quadratic forms, it exhibits finite convergence, in certain cases. Numerical studies indicate that it is considerably superior to both the Davidon-Fletcher-Powell algorithm and the conjugate-gradient algorithm.     

含有等式约束非线性规划的全局优化算法

针对含有多个等式约束的非线性规划问题,提出一个全局优化算法.该方法基于可行集策略把改进的模拟退火方法与确定的局部算法方法相结合.对算法的收敛性进行了证明,数值结果表明算法的有效性及正确性.     

A Hybrid Genetic Algorithm with Boltzmann Convergence Properties

Stochastic global search algorithms such as genetic algorithms are used to attack difficult combinatorial optimization problems. However, genetic algorithms suffer from the lack of a convergence proof. This means that it is difficult to establish reliable algorithm braking criteria without extensive a priori knowledge of the solution space. The hybrid genetic algorithm presented here combines a genetic algorithm with simulated annealing in order to overcome the algorithm convergence problem. The genetic algorithm runs inside the simulated annealing algorithm and provides convergence via a Boltzmann cooling process. The hybrid algorithm was used successfully to solve a classical 30-city traveling salesman problem; it consistently outperformed both a conventional genetic algorithm and a conventional simulated annealing algorithm. This work was supported by the University of Colorado at Colorado Springs.     

Long-Step Primal Path-Following Algorithm for Monotone Variational Inequality Problems

In this paper, we present a long-step primal path-following algorithm and prove its global convergence under usual assumptions. It is seen that the short-step algorithm is a special case of the long-step algorithm for a specific selection of the parameters and the initial solution. Our theoretical result indicates that the long-step algorithm is more flexible. Numerical results indicate that the long-step algorithm converges faster than the short-step algorithm.     

Nonlinear Smoothing and the EM Algorithm for Positive Integral Equations of the First Kind

We study a modification of the EMS algorithm in which each step of the EMS algorithm is preceded by a nonlinear smoothing step of the form , where S is the smoothing operator of the EMS algorithm. In the context of positive integral equations (à la positron emission tomography) the resulting algorithm is related to a convex minimization problem which always admits a unique smooth solution, in contrast to the unmodified maximum likelihood setup. The new algorithm has slightly stronger monotonicity properties than the original EM algorithm. This suggests that the modified EMS algorithm is actually an EM algorithm for the modified problem. The existence of a smooth solution to the modified maximum likelihood problem and the monotonicity together imply the strong convergence of the new algorithm. We also present some simulation results for the integral equation of stereology, which suggests that the new algorithm behaves roughly like the EMS algorithm. Accepted 1 April 1997     

CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Mehrotra’s algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra’s algorithm. This paper describes a proposal and implementation of an alternative algorithm, an arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by the arc-search infeasible interior-point algorithm and Mehrotra’s algorithm, that the proposed arc-search infeasible interior-point algorithm is a more reliable and efficient algorithm than Mehrotra’s algorithm.     

Hybrid Flow-Shop: a Memetic Algorithm Using Constraint-Based Scheduling for Efficient Search

The paper considers the hybrid flow-shop scheduling problem with multiprocessor tasks. Motivated by the computational complexity of the problem, we propose a memetic algorithm for this problem in the paper. We first describe the implementation details of a genetic algorithm, which is used in the memetic algorithm. We then propose a constraint programming based branch-and-bound algorithm to be employed as the local search engine of the memetic algorithm. Next, we present the new memetic algorithm. We lastly explain the computational experiments carried out to evaluate the performance of three algorithms (genetic algorithm, constraint programming based branch-and-bound algorithm, and memetic algorithm) in terms of both the quality of the solutions produced and the efficiency. These results demonstrate that the memetic algorithm produces better quality solutions and that it is very efficient.