Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations

In this paper, we review briefly some methods for minimizing a functionF(x), which proceed by follwoing the solution curve of a system of ordinary differential equations. Such methods have often been thought to be unacceptably expensive; but we show, by means of extensive numerical tests, using a variety of algorithms, that the ODE approach can in fact be implemented in such a way as to be more than competitive with currently available conventional techniques.This work was supported by a SERC research studentship for the first author. Both authors are indebted to Dr. J. J. McKeown and Dr. K. D. Patel of SCICON Ltd, the collaborating establishment, for their advice and encouragement.     

OPTIMAL INSTAR PARASITIZATION IN A STAGE STRUCTURED HOST-PARASITOID MODEL

A stage structured host-parasitoid model is derived and the equilibria studied. It is shown under what conditions the parasitoid controls an exponentially growing host in the sense that a coexistence equilibrium exists. Furthermore, for host populations whose inherent growth rate is not too large it is proved that in order to minimize the adult host equilibrium level it is necessary that the parasitoids attack only one of the larval stages. It is also proved in this case that the minimum adult host equilibrium level is attained when the parasitoids attack that larval stage which also maximizes the expected number of emerging adult parasitoid per larva at equilibrium. Numerical simulations tentatively indicate that the first conclusion remains in general valid for the model. However, numerical studies also show that it is not true in general that the optimal strategy will maximize the number of emerging adult parasitoid per larva at equilibrium.     

Numerical analysis for the periodic response of nonsmooth dynamic systems of high-dimension

This paper deals with the numerical solution of high dimensional dynamic systems with nonsmooth characteristics, such as structural elastoplasticity, mechanical clearance and dry friction. As a stable periodic response of the system attracts its transient response, it may be extracted from the transient response somehow. The paper suggests a novel iteration scheme to extrapolate the periodic response from a short time history of its transient response by curve fitting. Compared with the current schemes such as shooting and incremental harmonic balancing, the present scheme makes full use of the information within the transient response and the system characters, then its computation efficiency has increased by an order and the numerical convergence depending on the initial iteration has greatly improved.The subject supported by the Chinese Foundation of Aeronautical Science     

Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces

A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wavccurrent field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does so by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best. Project supported by the Chinese Academy of Sciences.     

两个非线性方程的准确解

借助于计算机代数系统Ｍａｔｈｅｍａｔｉｃａ利用直接代数方法获得了两个有数学物理意义的非线性耗散－色散方程的准确解，这种方法也适用于高维非线性方程。     

金融时间序列分析与建模

介绍了金融时间序列分析与建模的主要理论、方法,着重论述了近20多年发展起来的非平稳时间序列的建模方法及工具,指出进一步的研究方向.最后,对上证综合指数这一金融时间序列进行了实证分析.     

解可分离约束双凹规划问题的一种外逼近方法[英文]

在本文中，我们提出了双凹规划问题和更一般的广义凹规划问题。我们给出了双凹规划问题的整体最优性条件，并构造了一个有限终止外逼近算法。     

NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD, the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1-and L2-norm space estimates and the 0((△t)2) estimate for time variable are obtained.     

箱覆盖问题的半定松驰算法

箱覆盖问题是NP困难问题中的经典问题，得到了广泛地研究，九十年代以来，半定松驰策略被用来求解组合优化问题，取得了很好的结果[13]，本文首次给箱覆盖问题的半定松驰算法，算法的理论分析结果表明它适合于求解大规模的箱覆盖问题。     

Consistency of a myopic Bayesian algorithm for one-dimensional global optimization

A sequential Bayesian method for finding the maximum of a function based on myopically minimizing the expected dispersion of conditional probabilities is described. It is shown by example that an algorithm that generates a dense set of observations need not converge to the correct answer for some priors on continuous functions on the unit interval. For the Brownian motion prior the myopic algorithm is consistent; for any continuous function, the conditional probabilities converge weakly to a point mass at the true maximum.