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A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
Sensitivity methods for the analysis of the outputs of discrete Bayesian networks have been extensively studied and implemented in different software packages. These methods usually focus on the study of sensitivity functions and on the…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
The multivariate generalized Gaussian distribution (MGGD), also known as the multivariate exponential power (MEP) distribution, is widely used in signal and image processing. However, estimating MGGD parameters, which is required in…
Although much progress has been made towards robust deep learning, a significant gap in robustness remains between real-world perturbations and more narrowly defined sets typically studied in adversarial defenses. In this paper, we aim to…
In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…
This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…
Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variational inequalities. Several results have been proved to extend…
A sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding. While sensitivity analyses in matched observational studies have been well addressed when there is a single outcome…
We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main…
Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…
In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation…
In this study, after given the definition of soft sets and their basic operations we define convex soft sets which is an important concept for operation research, optimization and related problems. Then, we define concave soft sets and give…
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…
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…
Many problems in high-dimensional statistics and optimization involve minimization over nonconvex constraints-for instance, a rank constraint for a matrix estimation problem-but little is known about the theoretical properties of such…
We consider sensitivity of a semidefinite program under perturbations in the case that the primal problem is strictly feasible and the dual problem is weakly feasible. When the coefficient matrices are perturbed, the optimal values can…
We investigate the properties of a class of piecewise-fractional maps arising from the introduction of an invariance under rescaling into convex quadratic maps. The subsequent maps are quasiconvex, and pseudoconvex on specific convex cones;…