Dual–primal proximal point algorithms for extended convex programming

This paper presents a class of dual–primal proximal point algorithms (PPAs) for extended convex programming with linear constraints. By choosing appropriate proximal regularization matrices, the application of the general PPA to the equivalent variational inequality of the extended convex programming with linear constraints can result in easy proximal subproblems. In theory, the sequence generated by the general PPA may fail to converge since the proximal regularization matrix is asymmetric sometimes. So we construct descent directions derived from the solution obtained by the general PPA. Different step lengths and descent directions are chosen with the negligible additional computational load. The global convergence of the new algorithms is proved easily based on the fact that the sequences generated are Fejér monotone. Furthermore, we provide a simple proof for the O(1/t) convergence rate of these algorithms.     

Compact difference method for solving the fractional reaction–subdiffusion equation with Neumann boundary value condition

In this paper, we derive a high-order compact finite difference scheme for solving the reaction–subdiffusion equation with Neumann boundary value condition. The L1 method is used to approximate the temporal Caputo derivative, and the compact difference operator is applied for spatial discretization. We prove that the compact finite difference method is unconditionally stable and convergent with order O(τ^2?α+h⁴) in L₂ norm, where τ, α, and h are the temporal step size, the order of time fractional derivative and the spatial step size, respectively. Finally, some numerical experiments are carried out to show the effectiveness of the proposed difference scheme.     

无线体域网高能效竞争接入机制研究

低能耗是无线体域网WBAN通信最重要的指标.构建了IEEE 802.15.6无线体域网CSMA/CA竞争接入的功耗模型,分析了用户优先级、MAC帧负荷尺寸和数据到达量对信道接入能耗的影响,提出了一种通过数据汇聚传输提高能量效率的增强型信道接入方法.仿真结果表明,在低业务量及混合业务场景下,所提方法能够显著减少信道接入的能量消耗.     

Software for estimation of second order effective material properties of porous samples with geometrical and physical nonlinearity accounted for

A method and an algorithm for numerical estimation of effective mechanical properties of porous materials are presented. The effective properties are sought in the form of the nonlinear relation between the second Piola–Kirchhoff stress tensor and the Green strain tensor for anisotropic materials with second-order nonlinearities accounted for. The effective characteristics of test models are computed by means of a CAE Fidesys program module based on the proposed algorithm. The effective material properties as functions of porosity are examined. The finite element mesh that contained more than a million of elements was used while performing stress analysis of a specimen. To reduce computing time, assembly and solution of the global equation system was done in parallel using CUDA technology. The computations were carried out on NVIDIA Tesla C2050 graphics processors. Our results show that accounting for nonlinear effects is essential for correct estimation of effective properties of porous materials.     

城市区域交通信号迭代学习控制策略

城市交通流具有复杂的非线性动态特性, 在交通控制中难以对其进行精确的数学建模; 同时, 以天为周期, 宏观交通流又呈现出明显的周期性特征. 鉴于此, 提出一种基于迭代学习的城市区域交通信号控制策略, 通过对交通信号的迭代控制, 使路段的平均占有率收敛于期望占有率, 从而使绿灯时间得到充分利用并防止交通拥堵的发生, 保证了交通流在路网中的高效平稳运行. 严格的理论推导证明了该方法的收敛性, 仿真结果验证了该方法的有效性.

     

复形态双向联想记忆网络及其性能分析

基于复数环(C,∨,∧,+)提出了复形态双向联想记忆网络模型,给出了神经网络实现双向完全联想记忆的条件,并分析了自联想的存储能力、稳定性和收敛性及神经网络的抗噪声能力.当复数虚部取零时即为实数,实数域形态双向联想记忆网络就是复数域形态双向联想记忆网络的特例.最后通过仿真实验验证复形态双向联想记忆网络的有效性.     

A cubic regularization algorithm for unconstrained optimization using line search and nonmonotone techniques

In recent years, cubic regularization algorithms for unconstrained optimization have been defined as alternatives to trust-region and line search schemes. These regularization techniques are based on the strategy of computing an (approximate) global minimizer of a cubic overestimator of the objective function. In this work we focus on the adaptive regularization algorithm using cubics (ARC) proposed in Cartis et al. [Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results, Mathematical Programming A 127 (2011), pp. 245–295]. Our purpose is to design a modified version of ARC in order to improve the computational efficiency preserving global convergence properties. The basic idea is to suitably combine a Goldstein-type line search and a nonmonotone accepting criterion with the aim of advantageously exploiting the possible good descent properties of the trial step computed as (approximate) minimizer of the cubic model. Global convergence properties of the proposed nonmonotone ARC algorithm are proved. Numerical experiments are performed and the obtained results clearly show satisfactory performance of the new algorithm when compared to the basic ARC algorithm.     

精英改进粒子群算法在入库堆垛问题中的应用

针对钢铁企业生产与物流一体化协同管理中入库堆垛问题,基于出库次序A型约束、垛位选择分散性约束等,建立了以均衡库存垛位负载和最大化板坯综合匹配度为目标的联合优化模型。结合问题的特点,基于PSO算法,利用收敛指数判断种群进化状态,并对处于"收敛"状态的种群执行精英学习策略,提高粒子的活性,帮助种群跃出局部最优。最后通过实例仿真说明了模型与算法的有效性和可行性。