A deterministic algorithm for global optimization

We present an algorithm for finding the global maximum of a multimodal, multivariate function for which derivatives are available. The algorithm assumes a bound on the second derivatives of the function and uses this to construct an upper envelope. Successive function evaluations lower this envelope until the value of the global maximum is known to the required degree of accuracy. The algorithm has been implemented in RATFOR and execution times for standard test functions are presented at the end of the paper.Partially supported by NSF DMS-8718362.     

Global attractor for a density-dependent sensitivity chemotaxis model

In this paper, a chemotaxi model with reproduction term in a bounded domain Ω ⊂ Rⁿ is discussed. The existence of a global-in-time solution and a global attractor for this model are obtained.     

Globally convergent algorithm for solving nonlinear equations

A general iterative method is proposed for finding the maximal rootx _max of a one-variable equation in a given interval. The method generates a monotone-decreasing sequence of points converging tox _max or demonstrates the nonexistence of a real root. It is globally convergent. A concrete realization of the general algorithm is also given and is shown to be locally quadratically convergent. Computational experience obtained for eight test problems indicates that the new method is comparable to known methods claiming global convergence.     

全局优化问题的一个无参数填充函数算法

填充函数法是求解全局优化问题的一种有效的确定性算法,方法的关键在于填充函数的构造.对于一般无约束优化问题提出了一个新的无参数填充函数,通过定义证明了此填充函数能保持填充性质.利用其理论性质设计了相应的算法并对几个经典的算例进行了数值实验,实验结果表明算法有效可行.     

Blowup,Global Fast and Slow Solutions for a Semilinear Combustible System

In this paper, we investigate a semilinear combustible system $u_t-du_{xx}=v^p, v_t-dv_{xx}=u^q$ with double fronts free boundary, where p ≥ 1, q ≥ 1. For such a problem, we use the contraction mapping theorem to prove the local existence and uniqueness of the solution. Also we study the blowup and global existence property of the solution. Our results show that when pq › 1 blowup occurs if the initial datum is large enough and the solution is global and slow, whose decay rate is at most polynomial if the initial value is suitably large, while when p › 1, q › 1 there is a global and fast solution, which decays uniformly at an exponential rate if the initial datum is small.     

求无约束连续全局优化问题的单参数填充函数法

填充函数法是求解全局优化问题的一个重要的确定性算法,这种方法的关键是构造具有良好性质的填充函数.构造了一个新的求解无约束全局优化问题的填充函数.函数连续可微且只包含一个参数.通过分析该函数的相关性质,设计了相应的算法.数值实验表明该算法简单有效.     

时滞Hopfield神经网络模型的全局吸引性和全局指数稳定性

对具有时滞的Hopfield神经网络模型,在非线性神经元激励函数是Lipschitz连续(而非已有的大部分文献中假设是Sigmoid函数)的条件下,通过构造适当的泛函,给出了这类模型全局吸引和平衡点全局指数稳定的易于验证的充分条件。     

Global existence and nonexistence results for a class of semilinear hyperbolic systems

In this paper, we investigate the Cauchy problem for a class of the system of semilinear hyperbolic equations with damping. With the use of the L_p → L_q type estimation for the corresponding linear problem and the method of comparison of functional, the existence and nonexistence criteria of global solutions are found. Copyright © 2012 John Wiley & Sons, Ltd.     

方程x_(n+1)=x_nexp[r_n((1-x_n)/(1-λx~n))]的全局吸引性

本文考虑非自治差分方程xn+ 1=xnexp[rn1- xn1-λxn]　 n=0 ,1,2 ,…的全局吸引性 ,这里 { rn}是正实数列 0 <λ<1我们获得了方程每一解趋于 1的充分条件 .     

The minimal criterion for the equivalence between local and global optimal solutions in nondifferentiable optimization problem

In the paper, a necessary and sufficient criterion it provided such that any local optimal solution is also global in a not necessarily differentiable constrained optimization problem. This criterion is compared to others earlier appeared in the literature, which are sufficient but not necessary for a local optimal solution to be global. The importance of the established criterion is illustrated by suitable examples of nonconvex optimization problems presented in the paper.     

一类有理递归序列的全局吸引性

研究递归序列xn 1=(a bxn-k)/(A-xn),n=0,1,…,的有界性,周期性和全局吸引性,其中a≥0,b,A>0为实数,初始条件x-k,…,x0为任意实数,得到方程的正平衡点是一个全局吸引子,且其吸引域依赖于参数的限制条件.     

A Free Boundary Problem of a Semilinear Combustible System with Higher Dimension and Heterogeneous Environment

In this paper, we investigate a free boundary problem of a semilinear combustible system with higher dimension and heterogeneous environment. Such a problem is usually used as a model to describe heat propagation in a two-component combustible mixture in which the free boundary is described by Stefan-like condition. For simplicity, we assume that the environment and solutions are radially symmetric. We use the contraction mapping theorem to prove the local existence and uniqueness of the solution. Also we study the blowup property and the long time behavior of the solution. Our results show that when pq › 1 blowup occurs if the initial datum is large enough and the solution is global and slow, whose decay rate is at most polynomial if the initial value is suitably large, while when p › 1, q › 1 there is a global and fast solution, which decays uniformly at an exponential rate if the initial datum is small.     

On existence and regularity of solutions for 2‐D micropolar fluid equations with periodic boundary conditions

In this paper, we prove the existence and uniqueness of a global solution for 2‐D micropolar fluid equation with periodic boundary conditions. Then we restrict ourselves to the autonomous case and show the existence of a global attractor. Copyright © 2006 John Wiley & Sons, Ltd.     

New Modified Function Method for Global Optimization

In this paper, a class of global optimization problems is considered. Corresponding to each local minimizer obtained, we introduced a new modified function and construct a corresponding optimization subproblem with one constraint. Then, by applying a local search method to the one-constraint optimization subproblem and using the local minimizer as the starting point, we obtain a better local optimal solution. This process is continued iteratively. A termination rule is obtained which can serve as stopping criterion for the iterating process. To demonstrate the efficiency of the proposed approach, numerical examples are solved.This research was partially supported by the National Science Foundation of China, Grant 10271073.     

Global well‐posedness and global attractor of fourth order semilinear parabolic equation

We study the initial boundary value problem of a class of fourth order semilinear parabolic equations. Global existence and nonexistence of solutions with initial data in the potential well are derived. Moreover, by using the iteration technique for regularity estimates, we obtain that for any k ≥ 0, the semilinear parabolic possesses a global attractor in H^k(Ω), which attracts any bounded subsets of H^k(Ω) in the H^k‐norm. Copyright © 2014 John Wiley & Sons, Ltd.     

A modified integral global optimization method and its asymptotic convergence

In this paper, we propose a new integral global optimization algorithm for finding the solution of continuous minimization problem, and prove the asymptotic convergence of this algorithm. In our modified method we use variable measure integral, importance sampling and main idea of the cross-entropy method to ensure its convergence and efficiency. Numerical results show that the new method is very efficient in some challenging continuous global optimization problems.     

Global attractors for the viscous hyperelastic‐rod wave equation

We consider the viscous hyperelastic‐rod wave equation subject to an external force, where the viscous term is given by second order differential operator in divergence form. Under some mild assumptions on the viscous term, first, we establish the global well‐posedness in both the periodic case and the case of the whole line, afterwards, we show the existence of global attractors for the two cases, respectively. Copyright © 2012 John Wiley & Sons, Ltd.     

一类具有脉冲控制的害虫管理SI数学模型研究

研究一类具有脉冲控制的害虫管理SI数学模型,运用Floquet理论证明了系统害虫灭绝周期解的全局渐近稳定性,并对所得结论进行了数值模拟.