Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares

Abstract A new Levenberg–Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM have been proposed, their main differences being in choice a damping parameter. In this paper, we propose rule updating parameter so as to achieve both global and local convergence even under presence constraint set. The key our results perspective from majorization-minimization methods. Specifically, show that if set specific way, objective function standard subproblem methods becomes an upper bound on original certain assumptions. Our solves sequence subproblems approximately using (accelerated) projected gradient method. It finds $$\varepsilon$$ ε -stationary point after $$O(\varepsilon ^{-2})$$ O ( - 2 ) computation achieves quadratic zero-residual error condition. Numerical compressed sensing matrix factorization converges faster many cases than existing