求解随机凸规划概率约束问题的对偶算法

1引言随机规划中的概率约束问题在工程和管理中有广泛的应用.因为问题中包含非线性的概率约束,它们的求解非常困难.如果目标函数是线性的,问题的求解就比较容易.给出了一个求解随机线性规划概率约束问题的综述.原-对偶算法和切平面算法是比较有效的.在本文中,我们讨论随机凸规划概率约束问题:     

相位阻尼下非X态的量子失协和几何失协

研究了在相位阻尼作用下非X态的量子失协与几何失协,用图像诠释了Bloch矢量以及相位阻尼系数p对失协的影响。通过讨论我们发现量子失协和几何失协都能在一段有限时间间隔内保持一定值,并且具有相同的突变点。量子失协和几何失协不会出现量子纠缠的突然死亡和重生现象,所以研究失协比纠缠更具有实际应用意义。     

振幅衰减模型中弱相干光场的退相干

利用热纠缠态表象求解密度矩阵主方程的方法,给出了任意时刻振幅衰减模型中弱相干场密度算符的表示式。采用数值计算方法计算了弱相干光场的压缩效应、统计性质和Wigner函数。讨论了耗散对这些量子特性的影响。研究结果表明:随衰减时间的增大,弱相干场的压缩效应、统计性质和Wigner函数的负性等非经典效应均减弱。     

Geometric discord for non-X states

The level surfaces of geometric discord for a class of two-qubit non-X states are investigated when the Bloch vectors are in arbitrary directions. The level surfaces of constant geometric discord are formed by three intersecting open tubes along three orthogc~nal directions. When Bloch vectors increase, the tubes along one or two directions shrink towards the center and may either totally disappear or the open tubes may become closed tubes when the Bloch vectors reach a critical value. In the generalized amplitude damping channel, the evolution of geometric discord shows double sudden changes when the parameter γ, increases. In the phase damping channel, the freezing phenomenon of geometric discord also exists.     

Coupled second order evolution equations with fading memory: Optimal energy decay rate

Of concern is the Cauchy problem for coupled second order semilinear evolution equations in a Hilbert space, with indirect memory-damping. We find an approach to obtain successfully an optimal rate of uniform decay for the system energy, only under basic conditions on the memory kernels. Simultaneously, the same rate is also obtained (with less difficulty) for the corresponding single memory-dissipative second order evolution equations. As can be seen, our results essentially improve the previously related ones in the literature. The abstract results are then applied to several concrete problems in the real world.     

Spectral analysis and exponential stability of one-dimensional wave equation with viscoelastic damping

This paper presents the exponential stability of a one-dimensional wave equation with viscoelastic damping. Using the asymptotic analysis technique, we prove that the spectrum of the system operator consists of two parts: the point and continuous spectrum. The continuous spectrum is a set of N points which are the limits of the eigenvalues of the system, and the point spectrum is a set of three classes of eigenvalues: one is a subset of N isolated simple points, the second is approaching to a vertical line which parallels to the imagine axis, and the third class is distributed around the continuous spectrum. Moreover, the Riesz basis property of the generalized eigenfunctions of the system is verified. Consequently, the spectrum-determined growth condition holds true and the exponential stability of the system is then established.     

The time constrained maximal covering salesman problem

We introduce the time constrained maximal covering salesman problem (TCMCSP) which is the generalization of the covering salesman and orienting problems. In this problem, we are given a set of vertices including a central depot, customer and facility vertices where each facility can supply the demand of some customers within its pre-determined coverage distance. Starting from the depot, the goal is to maximize the total number of covered customers by constructing a length constrained Hamiltonian cycle over a subset of facilities. We propose several mathematical programming models for the studied problem followed by a heuristic algorithm. The developed algorithm takes advantage of different procedures including swap, deletion, extraction-insertion and perturbation. Finally, an integer linear programming based improvement technique is designed to try to improve the quality of the solutions. Extensive computational experiments on a set of randomly generated instances indicate the effectiveness of the algorithm.     

A mathematical model for horizontal axis wind turbine blades

A mathematical model describing the nonlinear vibration of horizontal axis wind turbine (HAWT) blades is proposed in this paper. The system consists of a rotating blade and four components of deformation including longitudinal vibration (named axial extension), out-of-plane bend (named flap), in-plane/edgewise bend (named lead/lag) and torsion (named feather). It is assumed that the center of mass, shear center and aerodynamic center of a cross section all lie on the chord line, and do not coincide with each other. The structural damping of the blade, which is brought about by materials and fillers is taken into account based on the Kelvin–Voigt theory of composite materials approximately. The equivalent viscosity factor can be determined from empirical data, theoretical computation and experimental test. Gravitational loading and aerodynamic loading are considered as distributed forces and moments acting on blade sections. A set of partial differential equations governing the coupled, nonlinear vibration is established by applying the generalized Hamiltonian principle, and the current model is verified by previous models. The solution of equations is discussed, and examples concerning the static deformation, aeroelastic stability and dynamics of the blade are given.     

Partial Second-Order Subdifferentials in Variational Analysis and Optimization

This article presents a systematic study of partial second-order subdifferentials for extended-real-valued functions, which have already been applied to important issues of variational analysis and constrained optimization in finite-dimensional spaces. The main results concern developing extended calculus rules for these second-order constructions in both finite-dimensional and infinite-dimensional frameworks. We also provide new applications of partial second-order subdifferentials to Lipschitzian stability of stationary point mappings in parametric constrained optimization and discuss some other applications.     

Parallel algorithms for large-scale linearly constrained minimization problem

In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved.