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...     

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。     

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.     

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.     

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。     

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。     

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。     

Modified BCS Mechanism of Cooper Pair Formation in Narrow Energy Bands of Special Symmetry II. Matthias Rule Reconsidered

In part I of this paper a modified BCS mechanism of Cooper pair formation of electrons was proposed. This mechanism is connected with the existence of a narrow, roughly half-filled superconducting energy band of given symmetry. The special symmetry of the superconducting band was interpreted within a nonadiabatic extension of the Heisenberg model of magnetism. Within this nonadiabatic Heisenberg model, the electrons of the superconducting band are constrained to form Cooper pairs at zero temperature because in any normal conducting state the conservation of crystal-spin angular momentum would be violated. Except for this participation of the angular momentum, the pair formation is mediated in the familiar way by phonons. Superconducting bands can be identified even within a free-electron band structure. Therefore, in this paper the band structures of the bcc and hcp solid solution alloys composed of transition elements are approximated by appropriate free-electron band structures with s–d symmetry. From the free-electron bands, the number n of valence electrons per atom related to the maxima of the superconducting transition temperature T _c in these solid solutions is calculated within the nonadiabatic Heisenberg model. The two observed maxima of T _c are reproduced without any adjustable parameter at valence numbers n approximately equal to 4.9 and 6.5 in bcc and 4.7 and 6.7 in hcp solid solutions. This result is in good agreement with the measured values of 4.7 and 6.4 of Hulm and Blaugher. The upper maximum is predicted not to exist in bcc transition elements but to occur in several ordered structures of bcc solid solution alloys.     

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.     

Modified BCS Mechanism of Cooper Pair Formation in Narrow Energy Bands of Special Symmetry III. Physical Interpretation

In part I of this paper a modified BCS mechanism of Cooper pair formation was proposed. The present part III gives a physical interpretation of this mechanism in terms of spin-flipping processes in superconducting bands.     

Modified BCS Mechanism of Cooper Pair Formation in Narrow Energy Bands of Special Symmetry I. Band Structure of Niobium

The superconductor niobium possesses a narrow, roughly half-filled energy band with Bloch functions, which can be unitarily transformed into optimally localized spin-dependent Wannier functions belonging to a double-valued representation of the space group O ⁹ _h of Nb. The special symmetry of this superconducting band can be interpreted within a nonadiabatic extension of the Heisenberg model of magnetism. While the original Heisenberg model assumes that there is exactly one electron at each atom, the nonadiabatic model postulates that the Coulomb repulsion energy in narrow, partly filled energy bands is minimum when the balance between the bandlike and atomiclike behavior is shifted as far as possible toward the atomiclike behavior. Within this nonadiabatic Heisenberg model, the electrons of the superconducting band form Cooper pairs at zero temperature. Just as in the BCS theory of superconductivity, this formation of Cooper pairs is mediated by phonons. However, there is an important difference: within the nonadiabatic Heisenberg model, the electrons in a narrow superconducting band are constrained to form Cooper pairs because the conservation of spin angular momentum would be violated in any normal conducting state. There is great evidence that these constraining forces are responsible for superconducting eigenstates. This means that an attractive electron–electron interaction alone is not able to produce stable Cooper pairs. In addition, the constraining forces established within the nonadiabatic Heisenberg model must exist in a superconductor.     

Global optimization for the three-dimensional open-dimension rectangular packing problem

This article addresses the three-dimensional open-dimension rectangular packing problem (3D-ODRPP), which aims to pack a given set of unequal-size rectangular boxes within an enveloping rectangular space such that the volume of the occupied space is minimized. Even though the studied 3D-ODRPP is NP hard, the development of sophisticated global optimization methods has been stimulated. The mathematical programming formulation for the 3D-ODRPP has evolved into an effective and efficient mixed-integer linear programming (MILP) model. This study proposes an advanced exact scheme yielding a guaranteed global optimal solution given that all the instance data are non-negative rational numbers. The developed MILP retains not only fewer variables but also fewer constraints than the state-of-the-art models. The superior effectiveness and efficiency of the developed scheme are demonstrated with numerical experiments, where two sets of benchmark instances from references, real-world instances and instances with rational data are included.     

Prediction of Kinematic Viscosities for Binary and Ternary Liquid Mixtures with an ASOG-VISCO Group Contribution Method

The kinematic viscosities for 273 binary and 11 ternary systems were predicted with a new model (ASOG-VISCO) developed by combining the ASOG group contribution method and Eyrings theory of absolute reaction rates. The ASOG-VISCO group pair parameters were determined from literature kinematic viscosity data for group pairs of CH₂, ArCH, CyCH, OH, H₂O, CO, COO, CCl₃, and CCl₄ in the temperature range of 283.15 to 333.15 K. The overall average deviations between experimental and predicted kinematic viscosities for the binary and ternary systems were 4.15 and 5.03%, respectively. The predicted results using ASOG-VISCO were better than those determined with the UNIFAC-VISCO group contribution method.Paper presented at the Sixteenth European Conference on Thermophysical Properties, September 1–4, 2002, London, United Kingdom.