关键词： Mathematical programs with equilibrium constraints   Generalized project metric algorithm   Global convergence   Superlinear convergence  

摘要： This paper discusses a kind of mathematical programs with equilibrium constraints (MPEC for short). By using a complementarity function and a kind of disturbed technique, the original (MPEC) problem is transformed into a nonlinear equality and inequality constrained optimization problem. Then, we combine a generalized gradient projection matrix with penalty function technique to given a generalized project metric algorithm with arbitrary initial point for the (MPEC) problems. In order to avoid Mataros effect, a high-order revised direction is obtained by an explicit formula. Under some relative weaker conditions, the proposed method is proved to possess global convergence and superlinear convergence. (C) 2015 Published by Elsevier B.V.

关键词： Quantum measurement   Von Neumann algebras   Algebraic equations   Quantum efficiency (Physics)   Conditional probability   Quantum measure theory  

摘要： von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are, however, static processes that do not adapt to the states they measure. Advances in the field of adaptive measurement have shown that this limitation can be overcome by “wrapping” the von Neumann projectors in a higher-dimensional circuit which exploits the interplay between measurement outcomes and measurement settings. Unfortunately, the design of adaptive measurement has often been ad hoc and setup specific. We shall here develop a unified framework for designing optimized measurements. Our approach is twofold: The first is algebraic and formulates the problem of measurement as a simple matrix diagonalization problem. The second is algorithmic and models the optimal interaction between measurement outcomes and measurement settings as a cascaded network of conditional probabilities. Finally, we demonstrate that several figures of merit, such as Bell factors, can be improved by optimized measurements. This leads us to the promising observation that measurement detectors which—taken individually—have a low quantum efficiency can be arranged into circuits where, collectively, the limitations of inefficiency are compensated for.

关键词： Equilibrium constraints   Mathematical programs   QP-free algorithm   Global convergence   Superlinear convergence  

摘要： In this paper, based on the smoothing techniques and the working set techniques, a QP-free algorithm for mathematical programs with equilibrium constraints (MPEC for short) is presented. Firstly, by Fischer-Burmeister function and smoothing techniques, the discussed problem is approximated by a smooth constrained optimization problem. Secondly, the working set, which is used to construct systems of linear equations, is generated by pivoting operation. At each iteration, the search direction is yielded by solving two or three systems of equations with the same coefficient matrix. Under mild conditions, the global convergence and superlinear convergence are shown. Moreover, we can conclude that the current iterative point is an exact stationary point of the discussed problem if the proposed algorithm stops after finite iterations. Finally, preliminary numerical results are reported. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Max-plus algebra   The systems of inequalities   Eigenproblem   Finite solution   Proper supereigenvector   Algorithm  

摘要： This paper deals with the system of inequalities A circle times x >= x in which A is a square matrix, x is a column vector and circle times is a max-plus composition. It provides two algorithms which can be used to find a finite proper supereigenvectors of A corresponding to the eigenvalue lambda = 0 in a case of irreducible matrix A with the maximum cycle mean lambda(A) > 0 and a finite solution of the system in a case of reducible matrix A, respectively, in a polynomial number of steps. (C) 2015 Elsevier Inc. All rights reserved.

关键词： integrated scheduling   permutation flow-shop scheduling problem   transportation   mixed-integer linear programme (MILP)   swarm intelligence   anarchic society optimisation (ASO)   particle swarm optimisation (PSO)  

摘要： This paper addresses a permutation flow-shop scheduling problem where there are a finite number of transporters to carry jobs from each machine to its subsequent machine. The problem is first formulated as a mixed-integer linear programme, and then two anarchic society optimisation (ASO) algorithms are developed to solve large-sized instances of the problem. The numerical experience shows that the ASO algorithms are considerably effective and efficient. Finally, a sensitivity analysis is carried out to study the performance of the manufacturing system versus the transportation times and the number of transporters.

关键词： Hash算法   索引问题   数学模型   复杂度分析  

摘要： 针对查找DNA序列的相似序列问题,给出了建立索引和查找索引的数学模型,基于Hash算法,建立了依赖于k值大小的顺序索引模型和散列索引模型,特别对较大k值选用了DJBHash函数,有效的避免了Hash冲突问题。最后在硬件平台CPU为2.6GHz、内存为8G、操作系统为64位Windows 7的条件下,对100万条长度为100的DNA序列进行了测试,给出了不同k值下建立和查询索引的用时和占用内存情况,有效的解决了DNA序列的k-mer index问题。

关键词： 高中数学教学   算法思想   案例分析   思想渗透   数学内容   数学课程   基础知识   高考内容  

摘要： 在高中数学课程中，算法内容主要由两部分构成，一是集中介绍算法的基础知识，二是将算法思想分散渗透在相关数学内容中．近几年，浙江等省已不再将算法作为高考内容，人教社新课程修订的相关课题组也在研究《算法初步》是否独立成章的问题．

关键词： Book reviews   Nonfiction   Mathematics  

摘要： St. Clair reviews Things to Make and Do in the Fourth Dimension: A Mathematician's Journey through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More by Matt Parker.

关键词： 腧穴形态学   小波变换综合小电流   接地选线   算法  

摘要： 文章分析小波变换综合小电流接地故障信号的特点,并对小电流接地系统接地故障信号处理方法总结,分析了方法的适用范围和使用有点,将数学形态学的小波变换综合小电流接地选线算法提出。通过结合腧穴形态学的方法处理零序故障电流,将谐波分量和漂移量的干扰去除,对有效的系统故障信息获取,进而结合选线算法识别找出故障线路,通过仿真算例,方法可行性较高。