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.