On the Second-order Directional Derivatives of Singular Values of Matrices and Symmetric Matrix-valued Functions

The (parabolic) second-order directional derivatives of singular values of matrices and symmetric matrix-valued functions induced by real-valued functions play important roles in studying second-order optimality conditions for different types of matrix cone optimization problems. We propose a direct way to derive the formula for the second-order directional derivative of any eigenvalue of a symmetric matrix in Torki (Nonlinear Anal 46:1133–1150 2001), from which a formula for the second-order directional derivative of any singular value of a matrix is established. We demonstrate a formula for the second-order directional derivative of the symmetric matrix-valued function. As applications, the second-order derivative for the projection operator over the SDP cone is derived and used to get the second-order tangent set of the SDP cone in Bonnans and Shapiro (2000), and the tangent cone and the second-order tangent set of the epigraph of the nuclear norm are given as well.     

求解矩阵方程组的ABS算法

本文基于一类线性空间(Rn,n)n,n,建立求解( )X=B形式的矩阵方程组的ABS算法.讨论基本的ABS算法和两个特殊的ABS算法及其性质.并将其中的Huang算法用于求解带有各种约束(包括对称和稀疏约束)的拟牛顿方程.     

非线性约束优化问题的一个修正 Lagrangian 算法

基于一个含有控制参数的修正Lagrangian函数,该文建立了一个求解非线性约束优化问题的修正Lagrangian算法.在一些适当的条件下,证明了控制参数存在一个阀值,当控制参数小于这一阀值时,由这一算法产生的序列解局部收敛于问题的Kuhn-Tucker点,并且建立了解的误差上界.最后给出一些约束优化问题的数值结果.     

基于Unity3D的智能家居综合管理平台的研究与实现

利用Unity3D技术,对智能家居综合管理平台进行了优化,可根据用户的实际需要对空间进行建模,放弃了传统的二维平面管理平台,利用Unity3D对所需模型进行建模并且在所建立空间模型中实现了漫游,用户可对空间视野范围内的可控单元进行操作,实现了多目标实时控制.同时,虚拟现实技术其自身的特性增加了用户在使用时的沉浸感和互动性.     

MULTI-DIMENSIONAL MARKOV CHAIN–BASED ANALYSIS OF CONFLICT PROBABILITY FOR SPECTRUM RESOURCE SHARING

In this paper, we consider the optimal problem of channels sharing with heterogeneous traffic(real-time service and non-real-time service) to reduce the data conflict probability of users. Moreover, a multi-dimensional Markov chain model is developed to analyze the performance of the proposed scheme. Meanwhile, performance metrics are derived. Numerical results show that the proposed scheme can effectively reduce the forced termination probability, blocking probability and spectrum utilization.     

Structural stabilities, electronic, elastic and optical properties of SrTe under pressure: A first-principles study

The structural, electronic, elastic and optical properties as well as phase transition under pressure of SrTe have been systematically investigated by first-principles pesudopotential calculations. Five possible phases of SrTe have been considered. Our results show that SrTe undergoes a phase transition from NaCl-type (B1) to CsCl-type (B2) structure at 10.9 GPa with a volume collapse of 9.43%, and no further transition is found. We find that SrTe prefer h-MgO instead of wurtzite (B4) structure for its metastable phase because that the ionic compound prefers a high coordination. The elastic moduli, energy band structures, real and imaginary parts of the dielectric functions have been calculated for all considered phases, and we find that a smaller energy gap yields a larger high-frequency dielectric constant. Our calculated results are discussed and compared with the available experimental and theoretical data.     

关于Lipschitz强增生算子的迭代程序

本文在一般的Ｂａｎａｃｈ空间中讨论Ｌｉｐｓｃｈｉｔｚ强增生算子方程解和严格伪压缩算子不动点的迭代逼近问题．我们的结果统一和推广了Ｄｅｎｇ，Ｌｉｕ，Ｔａｎ和Ｘｕ的结果，完整地回答了Ｃｈｉｄｕｍｅ提出的公开问题．     

一类不可微优化的Fritz-John条件

基于星形集空间的性质,定义一类星形可微函数.这类函数是方向可微的,其方向导数可以表示成两个正齐次非负连续函数之差,其星形微分为一星形集对.对于含有不等式约束条件的星形可微优化问题,给出一个Fritz-John形式的最优性必要条件.     

一类新的含（A，η）-增生算子的广义混合拟-似变分包含组

介绍和研究了实q-一致光滑Banach空间中一类新的具（A,η）一增生算子的广义混合拟一似变分包含组,利用（A,η）一增生算子的预解算子技巧,证明了解的存在性及由新的P步迭代算法所生成序列的收敛性．     

实Banach空间中锥上的随机逼近和随机不动点定理

本文在实Ｂａｎａｃｈ空间的锥上证明了集值映射的随机逼近定理．作为应用，讨论了几个随机的不动点定理．我们的工作推广了Ｌｉｎ，Ｓｅｈｇａｌ和Ｓｉｎｇｈ的结果．