Using an Efficient Penalty Method for Solving Linear Least Square Problem with Nonlinear Constraints

In this paper, we use a penalty method for solving the linear least squares problem with nonlinear constraints. In each iteration of penalty methods for solving the problem, the calculation of projected Hessian matrix is required. Given that the objective function is linear least squares, projected Hessian matrix of the penalty function consists of two parts that the exact amount of a part of it is in the hand, but the calculation of the other part is expensive. In this paper, after obtaining a structured secant relation, we use a structured quasi-Newton method to approximate the projected Hessian matrix and then, we show the asymptotic and global convergence of the presented method. The obtained numerical results show the efficiency of this method.