A Derivative-Free Regularized Primal-Dual Interior-Point Algorithm for Constrained Nonlinear Least Squares Problems

We propose a derivative-free regularized primal-dual interior-point algorithm for nonlinear least squares problems with equality and inequality constraints. We approximate the Jacobian matrices of the residual function and constraint functions by the generalized finite difference, and incorporate the regularization scheme and least squares structure-exploiting into the primal-dual interior-point algorithm. It is shown that the algorithm converges to a KKT point of the problem or a stationary point of the constraints violation.