  In this paper we present a method for the regularized solution of nonlinear
inverse problems, based on Ivanov regularization (also called method of quasi
solutions or constrained least squares regularization). This leads to the
minimization of a non-convex cost function under a norm constraint, where
non-convexity is caused by nonlinearity of the inverse problem. Minimization is
done by iterative approximation, using (non-convex) quadratic Taylor expansions
of the cost function. This leads to repeated solution of quadratic trust region
subproblems with possibly indefinite Hessian. Thus the key step of the method
consists in application of an efficient method for solving such quadratic
subproblems, developed by Rendl and Wolkowicz [10]. We here present a
convergence analysis of the overall method as well as numerical experiments.
