Global optimization by random perturbation of the gradient method with a fixed parameter

The paper deals with the global minimization of a differentiable cost function mapping a ball of a finite dimensional Euclidean space into an interval of real numbers. It is established that a suitable random perturbation of the gradient method with a fixed parameter generates a bounded minimizing sequence and leads to a global minimum: the perturbation avoids convergence to local minima. The stated results suggest an algorithm for the numerical approximation of global minima: experiments are performed for the problem of fitting a sum of exponentials to discrete data and to a nonlinear system involving about 5000 variables. The effect of the random perturbation is examined by comparison with the purely deterministic gradient method.     

无严格互补松驰条件的序列线性方程组新算法

该文通过构造特殊形式的有效集来逼近KKT点处的有效集，给出了一个任意初始点下的序列线性方程组新算法，并证明了该算法在没有严格互补松驰条件的情况下具有全局收敛性和一步超线性收敛性。      

Near-optimal design of Global Positioning System (GPS) networks using the Tabu Search technique

This paper describes an optimization technique based on an heuristic procedure which is applied to analyse and improve the efficiency of the design of Global Positioning System (GPS) surveying networks. GPS is a valuable survey tool because of its ability to increase the accuracy, speed and flexibility of a survey. A GPS network can be defined as a number of stations, which are co-ordinated by a series of sessions, formed by placing receivers on stations. The goal is to select the best order in which these sessions can be organised to give the best possible schedule. Generally, solving large networks to optimality requires impractical computational time. This paper proposes a Tabu Search technique which provides optimal or near-optimal solutions for large networks with an acceptable amount of computational effort. Computational results for several case studies with known and unknown optimal schedules have been presented to assess the performance of the proposed technique.     

Global weak solutions to the Nordström-Vlasov system

The Nordström-Vlasov system is a Lorentz invariant model for a self-gravitating collisionless gas. We establish suitable a priori bounds on the solutions of this system, which together with energy estimates and the smoothing effect of “momentum averaging” yield the existence of global weak solutions to the corresponding initial value problem. In the process we improve the continuation criterion for classical solutions which was derived recently. The weak solutions are shown to preserve mass.     

Elliptic systems with nonlinearity q greater or equal than two with controlled growth. Global Hölder continuity of solutions to the Dirichlet problem

Hölder regularity up to the boundary of the solutions to the Dirichlet problem for second order elliptic systems with nonlinearity q>2 and with controlled growth is proved when n?q+2.     

无界区域R1上推广的B-BBM方程的整体吸引子

本文研究了无界区域R^1上推广的B—BBM方程的长时间动力学行为，证明了该方程整体吸引子的存在性．     

非线性应变波耦合组的吸引子的正则性

本文研究了非线性应变波方程与Schr(?)dinger方程耦合系统Cauchy问题吸引 子的正则性.获得了该系统在空间Eo中存在整体吸引子Ao,并且Ao与E1中的强吸 引子A1相等.     

具III类功能反应的非自治捕食扩散系统的全局稳定性(英文)

讨论了一类具有扩散率和 III类功能性反应的非自治捕食系统 ,证明了在适当条件下 ,系统是持久的 ,进一步如果系统是周期系统 ,则在一定条件下存在惟一全局稳定的周期解 .     

优化灰导数白化值的无偏灰色GM(1,1)模型

通过优化灰导数白化值 ,建立了无偏的 GM(1,1)模型 ,给出了估计模型参数的方法 ,证明了无偏GM(1,1)模型具有白指数律重合性 ,提出了新的预测公式 .实例分析表明 ,新方法提高了模型的精度 ,扩大了模型的适用范围 .     

周期二维Lotka—Volterra系统的一些新结果

该文研究周期二维Lotka－Volterra捕食食饵系统解的有界性，持续生存性以及正周期解的存在性和全局稳定性．并将结果推广到食饵有补充的周期二维Lotka－Volterra竞争系统上去，得到了一系列新的结果，改进和推广了文[1—3]的主要结论．