A variable projection-based parameter estimation algorithm for the nonsmooth separable nonlinear problems

In this paper, we consider the identification of RBF-type models with nonsmooth constraint, where the parameters can be partitioned into a linear part and a nonlinear part. Taking advantage of this special structure, we design a variable projection-based parameter estimation algorithm for the optimization of the RBF-type models with nonsmooth constraint. The proposed algorithm decomposes the original optimization problem into an inner subproblem and an outer subproblem. The linear parameters are eliminated by solving the easier solved inner problem, resulting in a reduced function that only contains nonlinear parameters. Then we separately utilize the proximal gradient method to optimize the linear parameters and trust region method to optimize the remaining nonlinear parameters. Simulation results on synthetic data and real-world data confirm the efficiency and effectiveness of the proposed algorithm.