一类连续最优控制问题的有限维近似

1　引　　言本文考虑具有状态终端约束、控制受限的非线性连续最优控制问题min　h0(x(0))+∫T0f0(x(t),u(t))dt+g0(x(T))(1.1)s.t.　x(t)=f(x(t),u(t)),　　t∈[0,T](1.2)D(x(0))=0,(1.3)E(x(T))=0,(1.4)S(u(t))≤0,　　t∈[0,T](1.5)其中,h0:Rn→R,f0:Rn×Rm→R,f:Rn×Rm→Rn,g0:Rn→R,D:Rn→Rp,E:Rn→Rq,S:Rm→Rr均为二次连续可微函数.T为终端时间(固定),p,q≤n,x(t)∈W1,∞[0,T]n,u(t)∈L∞[0,T]m分别为状态函数和控制函数.U(t)={u:S(u(t))≤0}为紧凸集.问题(1.1)—(1.5)要求寻找最佳控制u(t)使得目标函数(1.1)达到极小.…     

双障碍问题的逐次逼近阻尼牛顿法

1．引言及算法考虑Rn中的双障碍问题：求＊E年使其中f：Rn→Rn连续可微,c＝｛x-∈Rn|0≤x≤c｝,c∈Rn为常向量．若记c＝（c1,…,cn）T,则不准证明问题（1）等价于求解下面的非光滑方程组其中算子max,min是指分量的最大或最小．显然,由（2）式定义的函数H：Rn→Rn的第i个分量函数Hi：Rn→R为由（2）定义的函数H一般不是厂可微的,但我们可对H作如下分解：设住k｝是一单调递减且趋于O的正数序列,xk00,八k（）都是R”－＋R”的映射,其中bk（儿,W汕地分别由下式定义：其中圳的二v：二;＜人（x）一。k｝,B（x）二F：人（……     

预估-校正算法跟踪组合内点同伦路径

1.引 言 考虑下列凸数学规划（CNLP）问题 min f（x）,s.t.x ∈ Ω,（1.1）严格可行集合Ω0={x∈Rn:gi（x）<0,i=1,…,m}集合Ω表示Ω0的闭包,f（x）,gi（x）均为充分光滑函数.Ω的边界集合　Ω=Ω\Ω0,g=（g,…,gm）T,　x∈Ω,     

具无限时滞的积分微分方程的周期解的存在性、唯一性及稳定性

1引言考虑如下的Volterra积分微分方程其中t∈R，x∈Rn；A（t），C（t，s），C（t-S）都是n×n连续函数矩阵；f：R→Rn连续．关于方程（1．1）及（1．2）的周期解的存在性问题，已有不少研究工作[1-4]，例如[1]研究了当n＝1时方程（1．1）的周期解的存在性问题．得到了如下结果：定理A[1]如果下列条件满足：（i）A（t＋T），f（t＋T）=f（t），C（t＋T，s＋T）＝C（t；s）对t，s∈R成立，其中T＞0是常数．（ii）方程（1．1）具有“衰退记忆”．（iii）存在着常数K＞1及μ＞0使得A（t）＋K∫t-∞|C（t，s）|ds＜－μ则方程（1．1）…     

Boundedness of Marcinkiewicz integral related to multilinear commutators with variable kernels on Hardy spaces

Let→b=(b1,b2,…,bm),bi∈∧βi(Rn),1≤I≤m,βi＞0,m∑I=1βi=β,0＜β＜1,μΩ→b(f)(x)=(∫∞0|F→b,t(f)(x)|2dt/t3)1/2,F→b,t(f)(x)=∫|x-y|≤t Ω(x,x-y)/|x-y|n-1 mΠi=1[bi(x)-bi(y)dy.We consider the boundedness of μΩ,→b on Hardy type space Hp→b(Rn).     

仿射共轭梯度路径信赖域方法解有界约束优化

1 引言本文研究含有界变量约束的非线性优化问题 min f(x),x∈Ω (1．1) 其中f:Rn→R是光滑的非线性函数,约束可行集Ω=def{x∈Rn|li≤xi≤ui,i= 1,…,n},可行内点集int(Ω)=def{x∈Rn|li     

PERSISTENCE OF NONAUTONOMOUS COMPETITIVE SYSTEMS WITH INFINITE DELAY

Inthispaperweconsidernonlinear,nonautonomous,nonconvolutiontypeVolterrasystemoftheformForx=(x1,...,xn)∈Rn,wedefine.Weassumethat(A)Gi:R×R×Rn×Rn→R ismeasurableandthereexistsacontinuouspositivefunctionh:R-→ R suchthatandGi(t,s,0,0)≡0,andGi(t,s,x,y)is'nondecreasinginxjforfixedt,s,x1,...1xj-1,xj 1,...,xnandisnondecreasinginyiforfixedt,s,y1,...,yj-1,yj 1,...,yn,i,j=1,...,n.Wedefineandds,whereLetbethemetricspacewithop,Φ∈ChandeachofitscomponentsΦi(s)≥0fors≤0.Wealsoassumethatarecontin…     

A New Descent Method for Unconstrained Optimization Problem

Consider the unconstrained optimilzation problemminf(x), x E Rn, (1)where f: Rn - R1 is a continuously differentiable function. We denote the gradient function off by g(x) = f(x) and denote gb = g(xk), xk is an iterative point in descent method.The descent method has the following formXk 1 = Xk sk, (2)where sk = akdk, ak is a kind of stepsize and dk is a search direction such thatCos < -gb, dk >2 >, (3)where < -gk, dk > denotes the angle of -gk and dk, 0 < > 1. If ak is determined byArmij…     

GLOBAL CONVERGENCE OF NONMONOTONIC TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION

§ 1　 IntroductionIn this paper we study the following nonlinear equality constrained optimization prob-lem:minimize f(x) ,subjectto h(x) =0 ,(P)where h(x) =(h1 (x) ,h2 (x) ,...,hm(x) ) T,f and hi(i=1 ,2 ,...,m) are Rn→R twice conti-nously differentiable(m≤n) .Many authors have studied the problem(P) with trustregion method(see,references[1～ 3 ] ) .These methods have the same property:to enforce strict monotonicity for meritfunction at every iteration.Paper[4 ] shows thatstrictmonotonic …     

求非凸二次约束二次规划问题全局解的线性化方法

1引言 考虑如下非凸二次规划的全局优化问题: (QP):{min xTQox doTx,s.t.xTQix ditx≤bi,i=1,…,m,x∈S={x∈Rn:l≤x≤u}, 其中Qo,Qi是n阶实对称矩阵,do,di∈Rn,bi∈R,i=1,…,m;l=(l1,…,ln)T,u=(u1,…,un)T .     

乘子方法中的参数选择

Di Pillo和Grippo提出的含参数C〉0的增广Lagrangian函数中，使用了最大函数，该函数可能在无穷多个点处不可微．为了克服这个问题，濮定国在2004年提出了一类带新的NCP函数的乘子法．该方法在增广Lagrangian函数和原问题之间存在很好的等价性；同时该方法具有全局收敛性，且在适当假设下，具有超线性收敛率．但是在该方法中，要求参数C充分大．为了实现算法及提高算法效率，本文给出了一个有效选择参数C的方法．     

A globally convergent constrained quasi-Newton method with an augmented lagrangian type penalty function

The recently proposed quasi-Newton method for constrained optimization has very attractive local convergence properties. To force global convergnce of the method, a descent method which uses Zangwill's penalty function and an exact line search has been proposed by Han. In this paper a new method which adopts a differentiable penalty function and an approximate line is presented. The proposed penalty function has the form of the augmented Lagrangian function. An algorithm for updating parameters which appear in the penalty function is described. Global convergence of the given method is proved.     

几何对称法在求取某些区域格林函数中的应用

格林函数法是数学物理方程中一种常用的方法,适用于求解狄利克雷问题.针对几种特殊区域上的上狄利克雷问题,采用几何对称法求取这些区域对应的格林函数,该方法对于该区域上格林函数的求解是有效的.     

求解Lipschitz型规划全局极小点的改进的填充函数法

1 引言 考虑问题 (P)min(x), x∈Ω其中F:ΩR~n→R是局部Lipschitz函数,Ω为紧集,且F(x)在Ω内有极小点。文[1,2,3]在一定条件下给出了求解一般非光滑规划全局极小点的填充函数法,并给出了求解的全过程。本文根据文[1,2,3]的思想,为求解(P),结合函数的特点,给出了一种改进     

A filled function method with one parameter for unconstrained global optimization

The filled function method is considered as an efficient approach to solve the global optimization problems. In this paper, a new filled function method is proposed. Its main idea is as follows: a new continuously differentiable filled function with only one parameter is constructed for unconstrained global optimization when a minimizer of the objective function is found, then a minimizer of the filled function will be found in a lower basin of the objective function, thereafter, a better minimizer of the objective function will be found. The above process is repeated until the global optimal solution is found. The numerical experiments show the efficiency of the proposed filled function method.     

A series of the solutions for the Heisenberg ferromagnetic spin chain equation

The Heisenberg ferromagnetic spin chain equation is investigated. By applying the improved F‐expansion method (Exp‐function method) and the Jacobi elliptic method, respectively, a series of exact solutions is constructed. The parametric conditions of the existence for the solutions are presented. These solutions comprise periodic wave solutions, doubly periodic wave solutions, and dark and bright soliton solutions, which are expressed in several different function forms, namely, Jacobi elliptic function, trigonometric function, hyperbolic function, and exponential function. The results illustrate that the Exp‐function method is a powerful symbolic algorithm to look for new solutions for the nonlinear evolution systems.     

一个解不等式约束非线性规划问题的有效方法

本文提出了一个解不等式约束非线性规划问题有效方法．在这个方法中,考虑解一个等价Ｋｕｈｎ－Ｔｕｃｋｅｒ条件的非线性方程组．这个方程组中ＮＣＰ函数的使用消去了对应于不等式约束的Ｌａｇｒａｎｇｅ乘子的非负性．截断牛顿方法被用来解这个非线性方程组．为了保证全局收敛性,一个强健的损失函数被选为寻查函数,同时方法中插入修正最速下降方向．本文证明了方法的分Ｑ－二阶收敛性,同时指出新方法可以有效地解稀疏大规模非线性规划问题。     

求解极大极小问题的一种稳定的对数障碍函数法

给出求解极大极小问题的一种对数障碍函数法．为了消除牛顿方程的病态,本文引进Ｂｒｏｙｄｅｎ 和Ａｔｔｉａ 在求解约束优化问题时,为克服罚函数的病态所采取的一种策略,提高了算法的稳定性．对子问题的结束准则等对算法的效率有重要影响的技术细节,本文也进行了研究．     

Error estimates for the interpolating moving least-squares method in n-dimensional space

In this paper, the interpolating moving least-squares (IMLS) method is discussed in details. A simpler expression of the approximation function of the IMLS method is obtained. Compared with the moving least-squares (MLS) approximation, the shape function of the IMLS method satisfies the property of Kronecker δ function. Then the meshless method based on the IMLS method can overcome the difficulties of applying the essential boundary conditions. The error estimates of the approximation function and its first and second order derivatives of the IMLS method are presented in n-dimensional space. The theoretical results show that if the weight function is sufficiently smooth and the order of the polynomial basis functions is big enough, the approximation function and its partial derivatives are convergent to the exact values in terms of the maximum radius of the domains of influence of nodes. Then the interpolating element-free Galerkin (IEFG) method based on the IMLS method is presented for potential problems. The advantage of the IEFG method is that the essential boundary conditions can be applied directly and easily. For the purpose of demonstration, some selected numerical examples are given to prove the theories in this paper.     

基于g函数的多元copula的构造

针对目前多元copula的构造方法存在的局限性,提出了构造多元copula的新方法.本文首先定义的一类新的函数-g函数,基于g函数建立了2-copula的构造方法,并讨论了该方法的存在性与唯一性问题,然后将2-copula的构造方法直接扩展到n-copula构造的情形.最后给出了g函数的一种寻求方法,从而说明此copula构造方法的可行性.