In this paper we consider the iteratively regularized Gauss–Newton method for solving nonlinear ill-posed inverse problems. Under merely the Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an order optimal regularization method if the solution is regular in some suitable sense.

This paper develops a second-order Newton algorithm for nding local solutions of rank-constrained LMI problems in robust synthesis. The algorithm is based on a quadratic approximation of a suitably deened merit function and generates sequences of LMI feasible iterates. The main trust of the algorithm is that it inherits the good local convergence properties of Newton methods and thus overcome t...

Second order methods for optimization call for the solution of sequences of linear systems. In this survey we will discuss several issues related to the preconditioning of such sequences. Covered topics include both techniques for building updates of factorized preconditioners and quasi-Newton approaches. Sequences of unsymmetric linear systems arising in NewtonKrylov methods will be considered...

We present an efficient block-diagonal approximation to the Gauss-Newton matrix for feedforward neural networks. Our resulting algorithm is competitive against state-of-the-art first-order optimisation methods, with sometimes significant improvement in optimisation performance. Unlike first-order methods, for which hyperparameter tuning of the optimisation parameters is often a laborious proces...

We consider the task of estimating the relative pose (position and orientation) between a 3D object and its projection on a 2D image plane from a set of point correspondences. Our approach is to formulate the task as an unconstrained optimization problem on the intersection of the special orthogonal group and a cone, and exploit as much as possible the geometry of the underlying parameter space...

The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...

Full Waveform Inversion (FWI) methods use generally gradient based method, such as the nonlinear conjugate gradient method or more recently the l-BFGS quasi-Newton method. Several authors have already investigated the possibility of accounting more accurately for the inverse Hessian operator in the minimization scheme through Gauss-Newton or exact Newton algorithms. We propose a general framewo...

Quasi-Newton methods have played a prominent role, over many years, in the design of effective practical methods for the numerical solution of nonlinear minimization problems and in multi-dimensional zero-finding. There is a wide literature outlining the properties of these methods and illustrating their performance [e.g., [8]]. In addition, most modern optimization libraries house a quasi-Newt...

We propose an approach to solving two-dimensional linear and nonlinear boundary-value problems of statics for shallow shells based on the generalized method finite integral transformations Newton– Kantorovich–Raphson linearization. In case, application is reduced construction two with respect different variables in analyzed domain under assumption that kernels one transformation are transforms ...

This paper addresses detection and characterization of chemical vapor fugitive emissions in a nonscattering atmosphere by processing of remotely-sensed long-wavelength infrared spectra. The analysis approach integrates a parameterized signal model based on the radiative transfer equation with a statistical model for the infrared background. The maximum likelihood model parameter values are defi...