A parallel method for finding the global minimum of univariate functions

We describe a new parallel method for solving global optimization problems. The formulation of the decision rules of this method is presented. We examine convergence conditions of the proposed algorithm and establish conditions which guarantee a considerable speedup with respect to the sequential version of the algorithm. We also present some numerical experiments executed on Alliant FX/80 for one class of multiextremal functions.The authors are greatly indebted to R. G. Strongin who stimulated the fulfillment of this research. They also would like to thank the anonymous referees for their useful suggestions.The research of the first author was partially supported by Grant 9494/NC/89 from the Italian Government under the Italian-Soviet Agreement about the Cultural and Scientific Exchange in 1990–1991. He thanks the Systems Department, University of Calabria, where he was a Visitor.     

On a new stochastic global optimization algorithm based on censored observations

In this paper a new algorithm is proposed for global optimization problems. The main idea is that of modifying a standard clustering approach by sequentially sampling the objective function while adaptively deciding an appropriate sample size. Theoretical as well as computational results are presented.     

Cord-slope form of Taylor's expansion in univariate global optimization

Interval arithmetic and Taylor's formula can be used to bound the slope of the cord of a univariate function at a given point. This leads in turn to bounding the values of the function itself. Computing such bounds for the function, its first and second derviatives, allows the determination of intervals in which this function cannot have a global minimum. Exploiting this information together with a simple branching rule yields an efficient algorithm for global minimization of univariate functions. Computational experience is reported.The first and second authors have been supported by FCAR (Fonds pour la Formation de Chercheurs et l'Aide à la Recherche) Grant 92EQ1048 and AFOSR Grant 90-0008 to Rutgers University. The first author has also been supported by NSERC (Natural Sciences and Engineering Research Council of Canada) Grant to HEC and NSERC Grant GP0105574. The second author has been supported by NSERC Grant GP0036426, FCAR Grant 90NC0305, and a NSF Visiting Professorship for Women in Science at Princeton University. Work of the third author was done in part while he was a graduate student at the Department of Mathematics, Rutgers University, New Brunswick, New Jersey, USA and during a visit to GERAD, June–August 1991.     

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.     

非线性密度制约的Ⅱ类功能反应系统的定性分析

本文对具有非线性密度制约的Ⅱ类功能反应系统进行了定性分析,给出了平衡点全局渐近稳定和存在极限环的充分条件及生态解释,所得结果就其参数空间和相空间而言都是大范围的。     

Sequential stopping rules for the multistart algorithm in global optimisation

In this paper a sequential stopping rule is developed for the Multistart algorithm. A statistical model for the values of the observed local maxima of an objective function is introduced in the framework of Bayesian non-parametric statistics. A suitablea-priori distribution is proposed which is general enough and which leads to computationally manageable expressions for thea-posteriori distribution. Sequential stopping rules of thek-step look-ahead kind are then explicitly derived, and their numerical effectiveness compared.     

Stochastic global optimization methods part II: Multi level methods

In Part II of our paper, two stochastic methods for global optimization are described that, with probability 1, find all relevant local minima of the objective function with the smallest possible number of local searches. The computational performance of these methods is examined both analytically and empirically.     

红外热成像鱼眼镜头设计中若干特殊问题的处理

提出鱼眼镜头光阑球差的级数表达式及其基于有限差分的近似计算方法,解决了通常的光阑倒追方法面临的难题;讨论孔径光阑与入瞳的特殊"共轭"关系,分析了光阑彗差和像差渐晕;运用Aitkin插值技术填补"溢出"光线在像面上的落点,以保证像质函数定义的一致性,维持自动优化持续进展,从而克服频繁的光线"溢出"造成的严重困难;提出充分利用像差渐晕改善像面照度均匀性的方法;论述标定轴外光束边界的逐次渐近过程和运用入瞳距离变量实现孔径光阑位置全域优化的技术.     

Absolute line intensities of CO2 in the 3090-3920 cm region

Absolute line intensities of ¹³C¹⁶O₂ were retrieved from high-resolution Fourier transform spectra recorded in the region 3090-3920 cm⁻¹. The uncertainty of the line intensity determination is estimated to be between 3 and 5% for the strong lines. The global fittings of the observed line intensities within the framework of the effective operators approach have been performed, reaching the experimental accuracy. A comparison of newly measured line intensities with those found in the HITRAN database is presented.     

A Cahn-Hilliard model in a domain with non-permeable walls

We consider in this article a Cahn-Hilliard model in a bounded domain with non-permeable walls, characterized by dynamic-type boundary conditions. Dynamic boundary conditions for the Cahn-Hilliard system have recently been proposed by physicists in order to account for the interactions with the walls in confined systems and are obtained by writing that the total bulk mass is conserved and that there is a relaxation dynamics on the boundary. However, in the case of non-permeable walls, one should also expect some mass on the boundary. It thus seems more realistic to assume that the total mass, in the bulk and on the boundary, is conserved, which leads to boundary conditions of a different type. For the resulting mathematical model, we prove the existence and uniqueness of weak solutions and study their asymptotic behavior as time goes to infinity.