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We study the Tikhonov regularization for ill-posed non-linear operator equations in Hilbert scales. Our focus is on the interplay between the smoothness-promoting properties of the penalty and the smoothness inherent in the solution. The…

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…

This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…

The Tikhonov-Phillips method is widely used for regularizing ill-posed inverse problems mainly due to the simplicity of its formulation as an optimization problem. The use of different penalizers in the functionals associated to the…

In this short note, we discuss a goal-oriented multiobjective optimization problem for system performance assessment. The objective function for such optimization problem, which is usually a composite of different performance indices…

With the extensive application of submodularity, its generalizations are constantly being proposed. However, most of them are tailored for special problems. In this paper, we focus on quasi-submodularity, a universal generalization, which…

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…

Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…

We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…

Over the last two decades, submodular function maximization has been the workhorse of many discrete optimization problems in machine learning applications. Traditionally, the study of submodular functions was based on binary function…

Across machine learning (ML) sub-disciplines researchers make mathematical assumptions to facilitate proof-writing. While such assumptions are necessary for providing mathematical guarantees for how algorithms behave, they also necessarily…

Maximizing a single submodular set function subject to a cardinality constraint is a well-studied and central topic in combinatorial optimization. However, finding a set that maximizes multiple functions at the same time is much less…

In this paper two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to…

Many results related to quantitative problems in the metric theory of Diophantine approximation are asymptotic, such as the number of rational solutions to certain inequalities grows with the same rate almost everywhere modulo an asymptotic…

Recently, a method to compute the implicit equation of a parametrized hypersurface has been developed by the authors. We address here some questions related to this method. First, we prove that the degree estimate for the stabilization of…

There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…

This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…

Orthogonally invariant functions of symmetric matrices often inherit properties from their diagonal restrictions: von Neumann's theorem on matrix norms is an early example. We discuss the example of "identifiability", a common property of…

We present consistent algorithms for multiclass learning with complex performance metrics and constraints, where the objective and constraints are defined by arbitrary functions of the confusion matrix. This setting includes many common…