气溶胶粒子反演的约束优化方法

Constrained Optimization Methods for Inversion of Aerosol Particle Size Distribution Functions

气溶胶粒子大小分布是地球环境科学研究中最重要的方向之一。由数学物理模型来估计气溶胶的粒子分布是一个不适定的反问题,反演的目的就是用适定的问题来代替不适定问题,并获得原问题解的近似。本文研究气溶胶粒子分布的约束优化反演方法。首先探讨了问题的病态性,接着基于对待反演参数施加先验约束给出了正则化模型。在正则化的具体实现上,研究了带线搜索技巧的BFGS算法。数值试验表明了本文的算法可以用来稳定地求解气溶胶粒子分布的反演问题,基于正则化模型的BFGS方法可以很好地反演气溶胶粒子分布函数。

Aerosol particle size distribution function is a key environmental parameter.Retrieval of the aerosol particle size distribution function is an improperly posed inverse problem.To deal with this problem and obtain the stable approximation of the particle size distribution function,proper inversion technique is necessary.In this paper,the author studies the constrained optimization methods for retrieval of aerosol particle size distribution functions.The ill-conditioning properties are discussed and a regularizing model is established.To solve the minimization problem,the author develops a BFGS method.Numerical experiments indicate that the method introduced in this paper can be used for solving the inversion problem in retrieval of aerosol particle size distribution functions.