A hybrid method for solving the nonlinear least squares problem with linear inequality constraints

This paper presents a new method with trust region technique for solving the nonlinear least squares problem with linear inequality constraints. The method proposed in this paper stems from the one presented in a recent paper by the authors. The method successively constructs trust region constraints, which are ellipsoids centered at the iterative points, in such a way that they lie in the relative interior of the feasible region. Thus the method belongs to the class of interior point methods, and hence the authors may expect that the generated sequence approaches a solution smoothly without the combinatorial complications inherent to traditional active set methods. They establish a convergence theorem for the proposed method and show its practical efficiency by numerical experiments.