Related papers: On the iteratively regularized Gauss--Newton metho…
In recent years Landweber(-Kaczmarz) method has been proposed for solving nonlinear ill-posed inverse problems in Banach spaces using general convex penalty functions. The implementation of this method involves solving a (nonsmooth) convex…
For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed…
This article introduces an innovative mathematical framework designed to tackle non-linear convex variational problems in reflexive Banach spaces. Our approach employs a versatile technique that can handle a broad range of variational…
In this paper, we consider the asymptotical regularization with convex constraints for nonlinear ill-posed problems. The method allows to use non-smooth penalty terms, including the L1-like and the total variation-like penalty functionals,…
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
As second-order methods, Gauss--Newton-type methods can be more effective than first-order methods for the solution of nonsmooth optimization problems with expensive-to-evaluate smooth components. Such methods, however, often do not…
We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…
In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…
In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…
In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with uniformly convex objective. We introduce the notion of second-order condition number of a certain…
We explore the use of the Gauss-Newton method for optimization in shape learning, including implicit neural surfaces and geometry-informed neural networks. The method addresses key challenges in shape learning, such as the ill-conditioning…
Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…
Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such…
In this paper we first extend the diminishing stepsize method for nonconvex constrained problems presented in [4] to deal with equality constraints and a nonsmooth objective function of composite type. We then consider the particular case…
This article studies Gauss-Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
In this paper, we develop an interior-point method for solving a class of convex optimization problems with time-varying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system…