An Interior Method for Nonconvex Semidefinite Programs

In several applications, semidefinite programs arise in which the matrix depends nonlinearly on the unknown variables. We propose a new solution method for such semidefinite programs that also applies to other smooth nonconvex programs. The method is an extension of a primal predictor corrector interior method to nonconvex programs. The predictor steps are based on Dikin ellipsoids of a “convexified” domain. The corrector steps are based on quadratic subprograms that combine aspects of line search and trust region methods. Convergence results are given, and some preliminary numerical experiments suggest a high robustness of the proposed method.     

Interior-Point Algorithm for Linear Optimization Based on a New Kernel Function

In this paper,we design a primal-dual interior-point algorithm for linear optimization.Search directions and proximity function are proposed based on a new kernel function which includes neither growth...     

Interior-Point Methods in l 1 Optimal Sparse Representation Algorithms for Harmonic Retrieval

Atomic decomposition is an alternative method for frequency detection in harmonic signals. This type of method produces very concentrated solutions with few nonzero components. It can be used as an alternative to traditional approaches, such as, principal-components frequency estimation methods. In this paper, we consider the basis pursuit principle to find the representation (frequency) coefficients of a harmonic signal by minimizing the l ₁ norm. For the l ₁ minimization, we compare two interior-point methods. A primal-dual method, which consists of the perturbed optimality conditions of the linear program, results in solutions that are more accurate and sparse than using a primal (affine scaling) method to solve the same linear program. We contrast the solutions obtained by the interior-point methods using the size of the given data and a bound for perfect recovery of the harmonic signals to establish the better performance of the primal-dual method. In addition, experimental results are shown.     

多用户检测问题的半定规划方法

在码分多址系统中，求解多用户检测问题是重要环节，介绍了多用户检测问题的应用背景和发展现状，重点综述基于半定规划模型寻求多用户的检测问题次优解的几种重要方法，包括随机扰动法，坐标下降法，半定规划的割平面法和二次规划的分枝定界法等，结合数值实验，评价比较了这些方法的优缺点。     

求解最大割问题的半定规划松弛的可行方向法

本文对最大割问题的半定规划松弛提出一个可行方向法,并给出算法的收敛性证明。数值实验表明：与半定规划内点法相比,可行方向法更能有效地求解大规模的最大割问题的半定规划松弛。     

二次锥规划的一种非精确不可行内点算法

给出了二次锥规划的一种非精确不可行内点算法。该算法允许搜索方向有相对较大的误差,且不要求迭代点的可行性。在相对不精确的假设下,利用该算法可找到二次锥规划的ε-近似解。     

拓扑优化方法及其在微型柔性结构设计中的应用

介绍了连续体结构拓扑优化设计中常用的均匀化方法和渐进结构优化法的原理，对拓扑优化中出现的数值不稳定现象——棋盘格式、网格依赖性和局部极值——进行了分析，通过典型实例和笔者最近的研究工作说明了拓扑优化在微型柔性机构设计中的应用，最后对拓扑优化技术的发展进行了展望。     

Computerized IR Determination of Structural Group Composition for High-Boiling Oil Fractions

A computerized form is given of IR spectral determination for structural group composition in high-boiling oil fractions by Berthold's method (7 structural elements) and Kuklinskii's method (28 structural elements), which reduces the analysis time by factors of 3–4 and improves the accuracy.     

Continuous approximation of material distribution for topology optimization

In this paper, we propose a checkerboard‐free topology optimization method without introducing any additional constraint parameter. This aim is accomplished by the introduction of finite element approximation for continuous material distribution in a fixed design domain. That is, the continuous distribution of microstructures, or equivalently design variables, is realized in the whole design domain in the context of the homogenization design method (HDM), by the discretization with finite element interpolations. By virtue of this continuous FE approximation of design variables, discontinuous distribution like checkerboard patterns disappear without any filtering schemes. We call this proposed method the method of continuous approximation of material distribution (CAMD) to emphasize the continuity imposed on the ‘material field’. Two representative numerical examples are presented to demonstrate the capability and the efficiency of the proposed approach against some classes of numerical instabilities. Copyright © 2004 John Wiley & Sons, Ltd.     

层次分析法在拆除爆破方案优化中的应用研究

将AHP的定性分析和定量分析相结合的系统分析方法运用于拆除爆破方案优化中,为拆除爆破方案的优化选择提供了科学的依据.AHP法应用于大型工业钢筋混凝土结构拆除爆破的实例中.根据实际条件,整个大型工业结构倒塌的设计方向是最好的,实践证明爆破效果也是很好.     

钢铁企业供应链客户订单的组批优化技术研究

针对钢铁企业供应链中市场对产品的小批量、多样性需求与钢铁企业大批量生产的矛盾，提出了集批因子、计划种类和工作任务单的概念，把客户订单组批与企业内加工材料组批有机地结合起来，从而对客户订单进行组批优化，并在实际应用中取得了较好的效果。     

Bi-directional evolutionary structural optimization for design-dependent fluid pressure loading problems

This article presents an evolutionary topology optimization method for compliance minimization of structures under design-dependent pressure loads. In traditional density based topology optimization methods, intermediate values of densities for the solid elements arise along the iterations. Extra boundary parametrization schemes are demanded when these methods are applied to pressure loading problems. An alternative methodology is suggested in this article for handling this type of load. With an extended bi-directional evolutionary structural optimization method associated with a partially coupled fluid–structure formulation, pressure loads are modelled with hydrostatic fluid finite elements. Due to the discrete nature of the method, the problem is solved without any need of pressure load surfaces parametrization. Furthermore, the introduction of a separate fluid domain allows the algorithm to model non-constant pressure fields with Laplace's equation. Three benchmark examples are explored in order to show the achievements of the proposed method.     

面向畲族地区的创新发展模式设计

目的在社会发展的进程中,关注少数民族地区的生存问题,充分整合其特色的当地资源,以创新的发展模式来适应社会的进步,有利于少数民族文化的传承和发展。方法以人口较少的畲族为研究对象,对其历史背景、社会环境及文化内容等多方面进行研究。采用以设计介入的方式探究社会创新理论应用于少数民族地区文化传承中的可能性,并针对文成县畲族地区的具体情况进行调研,提炼出地区品牌以服务设计为导向的可持续创新方法,构建出符合当地情况并以文化发展为主的服务生态系统。结论社会创新可以成为少数民族地区发展的战略工具,以此来打造体验模式、民族品牌、生产模式及服务设计等各个层面,成为少数民族地区获得可持续发展的方法之一,进而拉动少数民族地区的经济发展,以期为其他少数民族地区的发展提供借鉴,促进各民族文化繁荣。     

An Enhanced Formulation of the Maximum Entropy Method for Structural Optimization

A numerical optimization method was proposed time ago by Templeman based on the maximum entropy principle. That approach combined the Kuhn-Tucker condition and the information theory postulates to create a probabilistic formulation of the optimality criteria techniques. Such approach has been enhanced in this research organizing the mathematical process in a single optimization loop and linearizing the constraints. It turns out that such procedure transforms the optimization process in a sequence of systems of linear equations which is a very efficient way of obtaining the optimum solution of the problem. Some examples of structural optimization, namely, a planar truss, a spatial truss and a composite stiffened panel, are presented to demonstrate the capabilities of the methodology.     

农业标准化中分层指标体系的结构表示与化简方法

根据农业标准化的需要,本研究建立了一种分层指标体系的结构表示和化简方法。在该方法中,分层指标体系的结构由拓扑矩阵和权重矩阵表示。通过化简,将分层指标体系转为单层指标体系,并得到各底层指标的综合权重。进而,可用决策评价方法对待评对象进行评价分析。     

Group‐theoretic exploitations of symmetry in computational solid and structural mechanics

The use of group theory in simplifying the study of problems involving symmetry is a well‐established approach in various branches of physics and chemistry, and major applications in these areas date back more than 70 years. Within the engineering disciplines, the search for more systematic and more efficient strategies for exploiting symmetry in the computational problems of solid and structural mechanics has led to the development of group‐theoretic methods over the past 40 years. This paper reviews the advances made in the application of group theory in areas such as bifurcation analysis, vibration analysis and finite element analysis, and summarizes the various implementation procedures currently available. Illustrative examples of typical solution procedures are drawn from recent work of the author. It is shown how the group‐theoretic approach, through the characteristic vector‐space decomposition, enables considerable simplifications and reductions in computational effort to be achieved. In many cases, group‐theoretic considerations also allow valuable insights on the behaviour or properties of a system to be gained, before any actual calculations are carried out. Copyright © 2009 John Wiley & Sons, Ltd.     

Logistic 组稀疏回归模型的 Bayes 建模及变分推断

在工程应用中,如数据挖掘、成本预测以及风险预测等,Logistic 回归是一类十分重要的预测方法．当前,大部分 Logistic 回归方法都是基于优化准则而设计,这类回归方法具有参数调试过程繁琐、模型解释性差、估计子没有置信区间等缺点．本文从 Bayes 概率角度研究 Logistic 组稀疏性回归的建模与推断问题．具体来说,首先利用高斯-方差混合公式提出 Logistic 组稀疏回归的 Bayes 概率模型;其次,通过变分 Bayes 方法设计出一个高效的推断算法．在模拟数据上的实验结果表明,本文所提出的方法具有较好的预测性能．     

现代数学方法在材料科学中的应用进展

简要介绍了有限元分析、分形理论、小波分析、拓扑学等现代数学方法在材料研究中的应用情况，指出现代数学方法将在材料中起着越来越重要的作用。     

A sensitivity-based coordination method for optimization of product families

This article provides an introduction to a decomposition-based method for the optimization of product families with predefined platforms. To improve the efficiency of the system coordinator, a new sensitivity-based coordination method (SCM) is proposed. The key idea in SCM is that the system level coordinates share variables by using sensitivity information to make trade-offs between the product subsystems. The coordinated shared variables are determined by minimizing the performance deviation with respect to the optimal design of subproblems and constraint violation incurred by sharing. Each subproblem has a significant degree of independence and can be solved in a simultaneous way. The numerical performance of SCM is investigated, and the results suggest that the new approach is robust and leads to a substantial reduction in computational effort compared with the analytical target cascading method. Then, the proposed methodology is applied to the structural optimization of a family of automotive body side-frames.     

Exploitation of symmetry in graphs with applications to finite and boundary elements analysis

We present explicit and parametric forms of transformation matrices for three well‐known and widely used symmetry groups: S₂, C_2v and C_4v. Group representation theory is the most powerful method for exploiting symmetry. We propose an efficient algorithm for systematic generation of reducible representations that can be combined linearly to obtain the projection operators. The exact column spaces of these projection operators are calculated and integrated through special orderings, leading to exact explicit and parametric forms of transformation matrices. The transformation matrices could be used directly for block diagonalization of single‐variable scalar field problems. Another algorithm is proposed to extend the application of the method to nonscalar and multivariable field problems. Finally, the generality and efficiency of the proposed method in relation to computation times and the accuracy of results are illustrated through examples from spectral decomposition, free vibration, buckling of FEMs and boundary element analysis of a symmetric field. Copyright © 2012 John Wiley & Sons, Ltd.