Related papers: Regularisation, optimisation, subregularity
Block-coordinate descent (BCD) is a popular framework for large-scale regularized optimization problems with block-separable structure. Existing methods have several limitations. They often assume that subproblems can be solved exactly at…
We propose and analyze a perturbative regularization method to approximate quadratic optimization problems with finite-dimensional degeneracy. The original problem is first approximated by a regularized problem depending on a small positive…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…
Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued…
In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most successful optimisation methods in machine learning, imaging and…
This work presents a comprehensive discretization theory for abstract linear operator equations in Banach spaces. The fundamental starting point of the theory is the idea of residual minimization in dual norms, and its inexact version using…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von…
We study the solutions of infinite dimensional linear inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to recover, while the data fitting term is a near arbitrary…
In this paper we explore the relation between distributionally robust learning and different forms of regularization to enforce robustness of deep neural networks. In particular, starting from a concrete min-max distributionally robust…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
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…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in…
We extend an implicit regularization scheme to be applicable in the $n$-dimensional space-time. Within this scheme divergences involving parity violating objects can be consistently treated without recoursing to dimensional continuation.…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
We study the extragradient method for solving vector quasi-equilibrium problems in Banach spaces, which generalizes the extragradient method for vector equilibrium problems and scalar quasi-equilibrium problems. We propose a regularization…
We investigate local optimality conditions of first and second order for integer optimal control problems with total variation regularization via a finite-dimensional switching point problem. We show the equivalence of local optimality for…
In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…