On convergence analysis of a derivative-free trust region algorithm for constrained optimization with separable structure

In this paper, we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure, where derivatives of the objective function are not available and can not be directly approximated. At each iteration, we construct a quadratic interpolation model of the objective function around the current iterate. The new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust region. The filter technique is used to ensure the feasibility and optimality of the iterative sequence. Global convergence of the proposed algorithm is proved under some suitable assumptions.