A MIXED SUPERLINEARLY CONVERGENT ALGORITHM WITH NONMONOTONE SEARCH FOR CONSTRAINED OPTIMIZATIONS

§ 1　 IntroductionConsider the optimization problemmin{ f(x) :gj(x)≤ 0 ,j∈ I,gj(x) =0 ,j∈ L,x∈ Rn} ,(1 )where f(x) ,gj(x) :Rn→R,j∈I∪L.I={ 1 ,2 ,...,m} ,L={ m 1 ,...,m p} .We know thatthe sequential quadratic programming(SQP) [1～ 4] is one of the mostef-ficient methods to solve problem(1 ) because of its superlinear convergence.In order toovercome the Maratos effect[5] ,SQP should solve two quadratic sub-programmings ateachiteration,which,however,causes the amountof computation…     

Second-order optimality conditions for minimizing a max-function

We study Chaney's and Ben-Tal-Zowe's second-order directional derivatives with applications in minimization problem for max-functions of the formh(x): = max {f(x, τ); τ ∈T},where T is a compact metricspace. We improve Kawasaki's result on necessary condition for such functions in the minimization problem.     

线性规划两阶段法的改进算法

将单纯形法与对偶单纯形法及其思想结合运用,对两阶段法引进人工变量的方式进行了改进,探索出一种最多引入一个人工变量,即可求得线性规划初始可行基的新算法,能有效地节约计算机的存储量和计算量。     

关于(F,ρ)-不变凸性函数多目标规划的充分性条件

本文给出了一类更一般的广义凸性函数的定义:(F,ρ)-不变凸性函数,并论证了其多目标规划关于有效解的充分性条件.本文的一些主要结论是对文献[2]～[5]中相应结论的改进和推广.     

The constructive technique and its application in solving a nonlinear reaction diffusion equation

A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear reaction diffusion equation which describes a real process in physics and in chemistry. Several exact solutions for the equation are acquired under certain circumstances.     

Entanglement in an anisotropic spin-1 Heisenberg chain

The entanglement in an anisotropic spin-1 Heisenberg chain with a uniform magnetic field is investigated. The ground-state entanglement will undergo two different kinds of transitions when the anisotropy \Delta and the amplitude of the magnetic field B are varied. The thermal entanglement of the nearest neighbour always declines when B increases no matter what the value of the anisotropy is. It is very interesting to note that the entanglement of the next-nearest neighbour can increase to a maximum at a certain magnetic field. Regardless of the boundary condition, the nearest-neighbour entanglement always decreases and approaches to a constant value when the size of the system is very large. The constant value of open boundary condition is much larger than that of periodic boundary condition.     

随机模拟化学反应系统的加速L-leap算法

提出了随机模拟化学反应系统的加速L-leap算法,该算法根据leap条件确定具有最大倾向函数的反应通道的反应次数,并利用二项分布随机数生成其它反应通道在当前leap时间区间内的反应次数．L-leap算法可更好地满足leap条件．数值模拟实验表明该算法能取得更好的模拟性能．     

A kind of bivariate spline space over rectangular partition and pure bending of thin plate

The mechanical background of the bivariate spline space of degree 2 and smoothness 1 on rectangular partition is presented constructively.Making use of mechan- ical analysis method,by acting couples along the interior edges with suitable evaluations, the deflection surface is divided into piecewise form,therefore,the relation between a class of bivariate splines on rectangular partition and the pure bending of thin plate is established.In addition,the interpretation of smoothing cofactor and conformality con- dition from the mechanical point of view is given.Furthermore,by introducing twisting moments,the mechanical background of any spline belong to the above space is set up.     

三维无网格法中权函数影响半径的优化

从函数逼近的角度建立三维无网格法中权函数影响半径的优化计算模型,针对一次基、二次基情形求解该模型.分析不同影响半径下函数的逼近误差,以及计算量、条件数等因素对无网格法计算性能的影响,结合数值试验,确认给出的权函数影响半径是有效、可靠、综合最优的.