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Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…
We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…
We extend the geometrical inverse approximation approach for solving linear least-squares problems. For that we focus on the minimization of $1-\cos(X(A^TA),I)$, where $A$ is a given rectangular coefficient matrix and $X$ is the approximate…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
We introduce Flower, a solver for linear inverse problems. It leverages a pre-trained flow model to produce reconstructions that are consistent with the observed measurements. Flower operates through an iterative procedure over three steps:…
Often in real-world datasets, especially in high dimensional data, some feature values are missing. Since most data analysis and statistical methods do not handle gracefully missing values, the first step in the analysis requires the…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
In this paper, we develop an optimization-based framework for solving coupled forward-backward stochastic differential equations. We introduce an integral-form objective function and prove its equivalence to the error between consecutive…
Model-based deep learning methods such as loop unrolling (LU) and deep equilibrium model}(DEQ) extensions offer outstanding performance in solving inverse problems (IP). These methods unroll the optimization iterations into a sequence of…
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…
Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…
In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other…
The recent literature on first order methods for smooth optimization shows that significant improvements on the practical convergence behaviour can be achieved with variable stepsize and scaling for the gradient, making this class of…
Multilevel methods are among the most efficient numerical methods for solving large-scale linear systems that arise from discretized partial differential equations. The fundamental module of such methods is a two-level procedure, which…
In this article, we establish a class of new projected type iteration methods based on matrix spitting for solving the linear complementarity problem. Also, we provide a sufficient condition for the convergence analysis when the system…
We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
This paper is concerned with the nonnegative inverse eigenvalue problem of finding a nonnegative matrix such that its spectrum is the prescribed self-conjugate set of complex numbers. We first reformulate the nonnegative inverse eigenvalue…
This work assesses both empirically and theoretically, using the performance estimation methodology, how robust different first-order optimization methods are when subject to relative inexactness in their gradient computations. Relative…
One-shot image classification aims to train image classifiers over the dataset with only one image per category. It is challenging for modern deep neural networks that typically require hundreds or thousands of images per class. In this…