相关论文: Generalized Qualification and Qualification Levels…

A learning approach to selecting regularization parameters in multi-penalty Tikhonov regularization is investigated. It leads to a bilevel optimization problem, where the lower level problem is a Tikhonov regularized problem parameterized…

These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…

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…

During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…

Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert…

We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…

The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…

We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these conditions, we provide a unified global…

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000)…

Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…

Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again…

During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be…

Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated…

We present a regularization method to approach a solution of the pessimistic formulation of ill -posed bilevel problems . This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and…

The inherent ill-posed nature of image reconstruction problems, due to limitations in the physical acquisition process, is typically addressed by introducing a regularisation term that incorporates prior knowledge about the underlying…

For an arbitrary finite family of semi-algebraic/definable functions, we consider the corresponding inequality constraint set and we study qualification conditions for perturbations of this set. In particular we prove that all positive…

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

By the recent advances in computer technology leading to the invention of more powerful processors, the importance of creating models using data training is even greater than ever. Given the significance of this issue, this work tries to…

We investigate the generalizability of deep learning based on the sensitivity to input perturbation. We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to…