Related papers: On the convergence of an inertial proximal algorit…
Primal-dual splitting involving proximity operators in order to be able to find some approximation to the minimizer for a general form of Tikhonov type functional is in the focus of this work. This approximation is produced by a pair of…
In the framework of real Hilbert spaces, we investigate first-order dynamical systems governed by monotone and continuous operators. We demonstrate that when the monotone operator flow is augmented with a Tikhonov regularization term, the…
In this paper, in the setting of Hilbert spaces, we consider a Tikhonov regularized second-order plus first-order primal-dual dynamical system with asymptotically vanishing damping for a linear equality constrained convex optimization…
We study the convergence rate of the proximal-gradient homotopy algorithm applied to norm-regularized linear least squares problems, for a general class of norms. The homotopy algorithm reduces the regularization parameter in a series of…
In a separable Hilbert space, we study the minimization problem of a convex smooth function with Lipschitz continuous gradient whose evaluations are corrupted by random noise. To this end, we associate a stochastic inertial system that…
This paper focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of $f$…
We investigate an inertial algorithm of gradient type in connection with the minimization of a nonconvex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We prove some…
In a Hilbert framework, we consider an inertial Tikhonov regularized dynamical system governed by a maximally comonotone operator, where the damping coefficient is proportional to the square root of the Tikhonov regularization parameter.…
We present a new approach to convexification of the Tikhonov regularization using a continuation method strategy. We embed the original minimization problem into a one-parameter family of minimization problems. Both the penalty term and the…
Convergence rates in spectral regularization methods quantify the approximation error in inverse problems as a function of the noise level or the number of sampling points. Classical strong convergence rate results typically rely on source…
We propose a slowly damped inertial primal-dual dynamical system controlled by a Tikhonov regularization term, where the inertial term is introduced only for the primal variable, for the linearly constrained convex optimization problem in a…
Tikhonov regularization with square-norm penalty for linear forward operators has been studied extensively in the literature. However, the results on convergence theory are based on technical proofs and difficult to interpret. It is also…
In a Hilbert space setting $\mathcal H$, we study the convergence properties as $t \to + \infty$ of the trajectories of the second-order differential equation \begin{equation*} \mbox{(AVD)}_{\alpha, \epsilon} \quad \quad \ddot{x}(t) +…
One of the key assumptions in the stability and convergence analysis of variational regularization is the ability of finding global minimizers. However, such an assumption is often not feasible when the regularizer is a black box or…
We investigate the strong and the weak convergence properties of the following gradient projection algorithm with Tikhonov regularizing term \[ x_{n+1}=P_{Q}(x_{n}-\gamma_{n}\nabla f(x_{n})-\gamma_{n}\alpha_{n}\nabla \phi (x_{n})), \] where…
Tikhonov regularization is a popular approach to obtain a meaningful solution for ill-conditioned linear least squares problems. A relatively simple way of choosing a good regularization parameter is given by Morozov's discrepancy…
In this paper, we propose a general Tikhonov regularized second-order dynamical system with viscous damping, time scaling and extrapolation coefficients for the convex-concave bilinear saddle point problem. By the Lyapunov function…
We study the behaviour of Tikhonov regularisation on topological spaces with multiple regularisation terms. The main result of the paper shows that multi-parameter regularisation is well-posed in the sense that the results depend…
In a Hilbert setting we aim to study a second order in time differential equation, combining viscous and Hessian-driven damping, containing a time scaling parameter function and a Tikhonov regularization term. The dynamical system is…
We investigate a Tikhonov regularization scheme specifically tailored for shallow neural networks within the context of solving a classic inverse problem: approximating an unknown function and its derivatives within a unit cubic domain…