组合同伦方法在无界域上的收敛性

组合同伦内点法由Feng等提出，是求解有界区域上的非凸数学规划的一种大范围收敛性方法，本文证明此算法适用于某些无界区域上的非凸数学规划问题。     

A New Filled Function Method for Global Optimization

A novel filled function is suggested in this paper for identifying a global minimum point for a general class of nonlinear programming problems with a closed bounded domain. Theoretical and numerical properties of the proposed filled function are investigated and a solution algorithm is proposed. The implementation of the algorithm on several test problems is reported with satisfactory numerical results.     

Two-level primal–dual proximal decomposition technique to solve large scale optimization problems

We describe a primal–dual application of the proximal point algorithm to nonconvex minimization problems. Motivated by the work of Spingarn and more recently by the work of Hamdi et al. about the primal resource-directive decomposition scheme to solve nonlinear separable problems. This paper discusses some local results of a primal–dual regularization approach that leads to a decomposition algorithm.     

序约束下AR(p)-ARCH(q)模型参数的估计与检验

In this paper, we study a stationary AR(p)-ARCH(q) model with parameter vectors a and β. We propose a method for computing the maximum likelihood estimator (MLE) of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order: α1≥α2≥…≥αq, andβ1≥β2≥…βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio (LR) test statistic for the testing problem and derive its asymptotic null distribution.     

Two-Phase Image Segmentation by Nonconvex Nonsmooth Models with Convergent Alternating Minimization Algorithms

Two-phase image segmentation is a fundamental task to partition an image into foreground and background. In this paper, two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segmentation. They extend the convex regularization on the characteristic function on the image domain to the nonconvex case, which are able to better obtain piecewise constant regions with neat boundaries. By analyzing the proposed non-Lipschitz model, we combine the proximal alternating minimization framework with support shrinkage and linearization strategies to design our algorithm. This leads to two alternating strongly convex subproblems which can be easily solved. Similarly, we present an algorithm without support shrinkage operation for the nonconvex Lipschitz case. Using the Kurdyka-Łojasiewicz property of the objective function, we prove that the limit point of the generated sequence is a critical point of the original nonconvex nonsmooth problem. Numerical experiments and comparisons illustrate the effectiveness of our method in two-phase image segmentation.     

微机结构分析的现状与前景

本文回顾了16位微机上的通用结构分析系统近十年来国际、国内的发展概况,对未来十年微机结构分析的发展与前景提出了一些看法。在未来十年中,微机上的非线性结构分析将不仅成为可能,而且会成为计算力学主要的开发对象。非线性分析的求解器、分叉问题等非常棘手的问题,可望在未来十年中得到解决。多窗口图形系统等现代计算机技术将会使微机结构分析的用户界面增辉生色。     

论地质灾害防治工程的地质观与工程观

概括前人的经验, 结合作者个人的实践, 本文较详细地讨论了地质灾害防治工程的地质观念与工程观念。提出地质观的核心问题是地质灾害体的变形破坏力学机理分析, 工程观观与工程观运用的最佳耦合。文中还讨论了超前预测的作用, 监测反馈与工程效果检验的关系, 以及地质工程师与设计工程师的关系等, 最后以链子崖危岩体防治工程为例进行了说明。     

Focusing on the Needs: Experiences of Developing a Data Science Program

Donoho’s article “50 Years of Data Science” is a well-thought explanation of a newly developed discipline called “data science.” In this article, we examine his explanations and suggestions about data science, follow-up on some of the issues he mentioned, and share our experiences in developing a data science curriculum and the teaching of related courses.     

Evolutionary Boussinesq model with nonmonotone friction and heat flux boundary conditions

In this paper we prove the existence and regularity of a solution to a two-dimensional system of evolutionary hemivariational inequalities which describes the Boussinesq model with nonmonotone friction and heat flux. We use the time retardation and regularization technique, combined with a regularized Galerkin method, and recent results from the theory of hemivariational inequalities.     

Effects of awareness program and delay in the epidemic outbreak

In the present paper, an epidemic model has been proposed and analyzed to investigate the impact of awareness program and reporting delay in the epidemic outbreak. Awareness programs induce behavioral changes within the population, and divide the susceptible class into two subclasses, aware susceptible and unaware susceptible. The existence and the stability criteria of the equilibrium points are obtained in terms of the basic reproduction number. Considering time delay as the bifurcating parameter, the Hopf bifurcation analysis has been performed around the endemic equilibrium. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are investigated by using the normal form theory and central manifold theorem. To verify the analytical results, comprehensive numerical simulations are carried out. Copyright © 2016 John Wiley & Sons, Ltd.