A filter secant method with nonmonotone line search for equality constrained optimization

<正> This paper proposes a filter secant method with nonmonotone line search for non-linearequality constrained optimization.The Hessian of the Lagrangian is approximated using the BFGSsecant update.This new method has more flexibility for the acceptance of the trial step and requires lesscomputational costs compared with the monotone one.The global and local convergence of the proposedmethod are given under some reasonable conditions.Further,two-step Q-superlinear convergence rateis established by introducing second order correction step.The numerical experiments are reported toshow the effectiveness of the proposed algorithm.     

A line search filter secant method for nonlinear equality constrained optimization

<正> This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for searchdirection.The feature of the new algorithm is that the secant algorithm is used to produce a searchdirection,a backtracking line search procedure is used to generate step size,some filtered rules areused to determine step acceptance,second order correction technique is used to reduce infeasibility andovercome the Maratos effect.Global convergence properties of this method are analyzed:under mildassumptions it is showed that every limit point of the sequence of iterates generated by the algorithmis feasible,and that there exists at least one limit point that is a stationary point for the problem.Moreover,it is also established that the Maratos effect can be overcome in our new approach by addingsecond order correction steps so that fast local superlinear convergence to a second order sufficient localsolution is achieved.Finally,the results of numerical experiments are reported to show the effectivenessof the line search filter secant method.     

A TRUST REGION ALGORITHM WITH NULL SPACE TECHNIQUE FOR EQUALITY CONSTRAINED OPTIMIZATION

This paper presents a trust region algorithm with null space technique fornonlinear equality constrained optimization. Considering in the null space methods that,the convergent rate of range space step is faster than the null space step for the most cases,the proposed algorithm computes null steps more often than range space step. Moreover,the new algorithm is based on the reduced Hessian SQP method. Global convergence ofthe proposed algorithm is proved. The effectiveness of the method is demonstrated bysome numerical examples.     

改进的低时延全回波Q路由算法

针对传统路由算法不能适应拓扑环境及网络负载变化导致的拥塞问题,提出了一种改进的低时延全回波Q路由算法。改进算法对于原有算法附加学习率因子进行替换,使用调节范围更大、适应性更好、算法性能更稳健的双曲正割算子;改进算法根据不同网络情况自适应地调节学习率,进而提供合理的路由决策。仿真结果表明,该算法可以适应于静、动态拓扑环境,与已有的路由算法相比,改进算法能有效地减少高、低负载时数据的平均递交时间,降低路由间的振荡,提高数据包的投递率,且体现更好的稳健性。     

The determination on weight hierarchies of <Emphasis Type="Italic">q</Emphasis>-ary linear codes of dimension 5 in class IV

The weight hierarchy of a linear [n; k; q] code C over GF(q) is the sequence (d ₁, d ₂, ···, d _k ) where d _r is the smallest support of any r-dimensional subcode of C. “Determining all possible weight hierarchies of general linear codes” is a basic theoretical issue and has important scientific significance in communication system. However, it is impossible for q-ary linear codes of dimension k when q and k are slightly larger, then a reasonable formulation of the problem is modified as: “Determine almost all weight hierarchies of general q-ary linear codes of dimension k”. In this paper, based on the finite projective geometry method, the authors study q-ary linear codes of dimension 5 in class IV, and find new necessary conditions of their weight hierarchies, and classify their weight hierarchies into 6 subclasses. The authors also develop and improve the method of the subspace set, thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV. It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes (classes III and VI), and break through the difficulties. Furthermore, the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough (not most tight nor best), so, it is important to excogitate further new necessary conditions for attacking and solving the k-dimensional problem.     

NONMONOTONIC TRUST REGION PROJECTED REDUCED HESSIAN ALGORITHM WITH TWO-PIECE UPDATE FOR CONSTRAINED OPTIMIZATION

This paper proposes a two-piece update of projected reduced Hessian algorithm with nonmonotonic trust region strategy for solving nonlinear equality constrained optimization problems. In order to deal with large problems, a two-piece update of twoside projected reduced Hessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as the merit function, a nonmonotonic trust region strategy is suggested which does not require the merit function to reduce its value in every iteration. The two-piece update of projected reduced Hessian algorithm which switches to nonmonotonic trust region technique possesses global convergence while maintaining a two-step Q-superlinear local convergence rate under some reasonable conditions. Furthermore, one step Q-superlinear local convergence rate can be obtained if at least one of the update formulas is updated at each iteration by an alternative update rule. The numerical experiment results are reported to show the effectiveness of the propo     

Multitask n-vehicle exploration problem: Complexity and algorithm

This paper extends the single-task n-Vehicle Exploration Problem to Multitask n-Vehicle Exploration Problem(MTNVEP),by combining n-Vehicle Exploration Problem with Job Scheduling Problem.At first,the authors prove that MTNVEP is NP-hard for fixed number of tasks,and it is strongly NP-hard for general number of tasks.Then they propose an improved accurate algorithm with computing time O(n3~n),which is better than O(n!) as n becomes sufficiently large.Moreover,four heuristic algorithms are proposed.Effectiveness of the heuristic algorithms is illustrated by experiments at last.     

A FULL-NEWTON STEP INFEASIBLE INTERIOR-POINT ALGORITHM FOR P＊（κ） LINEAR COMPLEMENTARITY PROBLEM

This paper proposes a new infeasible interior-point algorithm with full-Newton steps for P＊（κ） linear complementarity problem（LCP）,which is an extension of the work by Roos（SIAM J.Optim.,2006,16（4）：1110-1136）.The main iteration consists of a feasibility step and several centrality steps.The authors introduce a specific kernel function instead of the classic logarithmical barrier function to induce the feasibility step,so the analysis of the feasibility step is different from that of Roos＇ s.This kernel function has a finite value on the boundary.The result of iteration complexity coincides with the currently known best one for infeasible interior-point methods for P＊（κ） LCP.Some numerical results are reported as well.     

Conditional Congruence Closure over Uninterpreted and Interpreted Symbols

A framework for generating congruence closure and conditional congruence closure of ground terms over uninterpreted as well as interpreted symbols satisfying various properties is proposed. It is based on some of the key concepts from Kapur’s congruence closure algorithm (RTA97) for ground equations based on introducing new symbols for all nonconstant subterms appearing in the equation set and using ground completion on uninterpreted constants and purified equalities over interpreted symbols belonging to different theories. In the original signature, the resulting rewrite systems may be nonterminating but they still generate canonical forms. A byproduct of this framework is a constant Horn completion algorithm using which ground canonical Horn rewrite systems can be generated for conditional ground theories.

New efficient algorithms for generating congruence closure of conditional and unconditional equations on ground terms over uninterpreted symbols are presented. The complexity of the conditional congruence closure is shown to be O(n*log(n)), which is the same as for unconditional ground equations. The proposed algorithm is motivated by our attempts to generate efficient and succinct interpolants for the quantifier-free theory of equality over uninterpreted function symbols which are often a conjunction of conditional equations and need additional simplification. A completion algorithm to generate a canonical conditional rewrite system from ground conditional equations is also presented. The framework is general and flexible and is used later to develop congruence closure algorithms for cases when function symbols satisfy simple properties such as commutativity, nilpotency, idempotency and identity as well as their combinations. Interesting outcomes include algorithms for canonical rewrite systems for ground equational and conditional theories on uninterpreted and interpreted symbols leading to generation of canonical forms for ground terms, constrained terms and Horn equations.

     

异步DS-CDMA最优混沌序列集的性能分析

为了获得异步DS—CDMA系统的最优扩谱序列，给出了一套用来选取混沌二值序列的优化准则。基于这一优化准则，我们从Chebyshev映射生成的混沌序列中选取并构造出最优混沌二值序列集合。利用该集合作为异步DS-CDMA系统的扩谱序列，所得到的系统仿真结果符合最优扩谱序列的理论分析值，因此可以被认为是异步DS-CDMA系统的一个最优扩谱序列集合。     

自适应试验遗传算法研究与应用

均匀设计与遗传算法相结合已有许多成功例子,但在应用中均匀设计表一般囿以固定形式而使二者的结合缺乏灵活性和普适性.为此提出应用亚遗传算法获得若干个任意水平数的均匀设计,并将其以3种方式嵌入标准遗传算法中:1)初始种群的均匀性分布;2)进化过程中对变量空间均匀性投点搜索;3)应用均匀设计进行调优试验,同时还增加了正态随机和摄动调优等试验操作技术,以上形成了基于试验设计、具有自适应能力的试验遗传算法.算例表明,通过以上方法改进的遗传算法可较好地保持种群多样性,寻优效率有较大提高,并能自动适应算法对搜索精度的要求.     

一种新的变步长LMS自适应滤波算法及性能分析

研究了自适应最小均方误差(least mean squares,LMS)滤波算法的步长选取问题。在详细分析现有变步长LMS算法的基础上,给出一种以双曲正切函数的改进形式为变步长的LMS算法。讨论了步长参数的选取原则及其对算法收敛性、抗干扰性和稳态误差的影响。该算法不但具有较快的收敛速度和跟踪速度,而且能获得更小的稳态失调。理论分析和仿真结果表明,该算法具有更好的稳态性能。     

基于自适应稀疏表示的高光谱遥感图像分类

针对多数传统分类算法应用于高光谱分类都存在运算速度慢、精度比较低和难以收敛等问题,从稀疏表示基本理论出发建立了一个基于自适应稀疏表示的高光谱分类模型。利用训练样本构建字典,聚类每一步迭代所产生的余项,将聚类中心作为新的字典原子,然后将测试样本看成冗余字典中训练样本的线性组合,令字典能够更适应于样本的稀疏表示。利用华盛顿地区的HYDICE高光谱遥感数据进行试验,并且与主成分分析、线性鉴别分析、支持向量机、神经网络算法进行比较,结果表明,该算法的总体分类精度比其他算法提高了约12%,有效提高了高光谱影像的分类精度。     

针对任意非高斯信号的快速固定点盲波束形成方法

峭度最大化盲波束形成算法的性能受步长调节参数的选择影响很大,尤其是在信道和信号参数未知的条件下,很难选择合适的步长。针对以上问题,提出了两种新的不需要步长调节参数,而且同样适用于任意非高斯信号的快速固定点的盲波束形成算法。首先通过白化对数据进行预先处理,然后以峭度最大化和波束形成器的权值正交化来构造代价函数,采用复数近似牛顿方法对代价函数优化,得到新的盲波束形成算法。与峭度最大化盲波束形成算法相比,该算法误差小、收敛速度快,不需要任何步长调节参数,更适用于信道和信号未知的环境。仿真实验验证了算法的有效性。     

The Ore-Sato Theorem and Shift Exponents in the q-Difference Case

The authors translate the main results in the paper entitled "Multiplicative Decomposition of Multivariate q-Hypergeometric Terms" from Chinese into English. The paper is written by Shaoshi Chen, Ruyong Feng, Guofeng Fu and Jing Kang, and published in Journal of Mathematics and Systems Science, 32(8), 1019–1032, 2012. Some minor simpli?cation and modi?cation are made during the translation. Based on the results in the above paper, a special form is derived for q-shift exponents appearing in the q-shift quotients of a q-hypergeometric term.     

NNMDS codes

C is an[n,k,d]_q linear code over F₉.And s（C）=n+1-k-d is the Singleton defect of C.An MDS code C with s（C）=0 has been studied extensively.Recently,a near-MDS code C with s（C）=s（C^⊥）=1 is studied by many scholars,where C^⊥denotes the dual code of C.This paper concentrates on the linear code C with s（C）=s（C^⊥）=2,and the author calls it an NNMDS code.A series of iff conditions of NNMDS codes are presented.And the author gives an upper bound on length of NNMDS codes.In the last,some examples of NNMDS are given.     

On LCD Negacyclic Codes over Finite Fields

This paper deduces the structure of LCD negacyclic codes over the finite field Fq, where q is an odd prime power. Based on the study of q-cyclotomic cosets modulo 2 n, the authors obtain the parameters of LCD negacyclic codes of lengths n =(q+1)/2,(q~m-1)/2(q-1)and q~(t·2~τ)-1/2(q~t +1), respectively. And many optimal codes are given. Moreover, the authors research two special classes of MDS LCD negacyclic codes of length n |(q-1)/2 and n |(q+1)2, respectively.     

A nonmonotone line search filter method with reduced Hessian updating for nonlinear optimization

This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization. In order to deal with large scale problems, a reduced Hessian matrix is approximated by BFGS updates. The new method assures global convergence without using a merit function. By Lagrangian function in the filter and nonmonotone scheme, the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved. The primary numerical experiments are reported to show effectiveness of the proposed algorithm.     

Inertial projection algorithms for convex feasibility problem

The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility problem.Compared with the existing accelerated methods for solving the problem,the inertial technique employs a parameter sequence and two previous iterations to get the next iteration and hence improves the flexibility of the algorithm.Theoretical asymptotic convergence results are presented under some suitable conditions.Numerical simulations illustrate that the new methods have better convergence than the general projection methods.The presented algorithms are inspired by the inertial proximal point algorithm for finding zeros of a maximal monotone operator.     

Enhancing the process of methodology choice in total systems intervention (TSI) and improving chances of tackling coercion

The process of Choice in TSI is reexamined in this paper. Previously, methods² have been understood to have a given and immediate purpose and are employed when this is judged to be most suitable in the circumstances. In this paper we suggest that methods can be operated in ways that meet purposes not provided by their founding theoretical underpinnings. We develop this argument by pointing to cases where cybernetic or soft methods are driven by purposes and principles given to emancipatory methodology—in a quest to address more effectively issues of coercion. This may be necessary when explicit and direct employment of emancipatory methodology is not sensitive enough to political dynamics, where certain people may feel overly threatened by its language and consequently feel the need to subvert its use. We develop a defence for thisoblique use of cybernetic and soft methods in coercive contexts, and extend the argument to suggest that all methods can be employed in such a way.