Related papers: On the convergence of an inertial proximal algorit…
Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov…
In this paper, we study the convergence properties of a randomized block-coordinate descent algorithm for the minimization of a composite convex objective function, where the block-coordinates are updated asynchronously and randomly…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…
The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…
We study a class of non-convex and non-smooth problems with \textit{rank} regularization to promote sparsity in optimal solution. We propose to apply the proximal gradient descent method to solve the problem and accelerate the process with…
We propose a new first-order optimisation algorithm to solve high-dimensional non-smooth composite minimisation problems. Typical examples of such problems have an objective that decomposes into a non-smooth empirical risk part and a…
In the paper, we study the convergence analysis of Tikhonov regularization in finding a zero of a maximal monotone operator using the notion of R-continuity. Applications to convex minimization and DC programming are provided.
Our focus is on the stable approximate solution of linear operator equations based on noisy data by using $\ell^1$-regularization as a sparsity-enforcing version of Tikhonov regularization. We summarize recent results on situations where…
We consider the proximal-gradient method for minimizing an objective function that is the sum of a smooth function and a non-smooth convex function. A feature that distinguishes our work from most in the literature is that we assume that…
We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…
We propose a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. The sequence of iterates generated by the algorithm converges to a…
We consider linear inverse problems that are formulated in the continuous domain. The object of recovery is a function that is assumed to minimize a convex objective functional. The solutions are constrained by imposing a continuous-domain…
We present a new approach to convergence rate results for variational regularization. Avoiding Bregman distances and using image space approximation rates as source conditions we prove a nearly minimax theorem showing that the modulus of…
We investigate the convergence properties of exact and inexact forward-backward algorithms to minimise the sum of two weakly convex functions defined on a Hilbert space, where one has a Lipschitz-continuous gradient. We show that the exact…
In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…
Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of…
We consider a variation of the classical proximal-gradient algorithm for the iterative minimization of a cost function consisting of a sum of two terms, one smooth and the other prox-simple, and whose relative weight is determined by a…
In a real Hilbert space setting, we investigate the asymptotic behavior of the solutions of the classical Arrow-Hurwicz differential system combined with Tikhonov regularizing terms. Under some newly proposed conditions on the Tikhonov…
Regular convergence, together with various other types of convergence, has been studied since the 1970s for the discrete approximations of linear operators. In this paper, we consider the eigenvalue approximation of compact operators whose…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…