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A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a…

Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine…

Bilevel optimization (BLO) problem, where two optimization problems (referred to as upper- and lower-level problems) are coupled hierarchically, has wide applications in areas such as machine learning and operations research. Recently, many…

The context of this paper is the simulation of parameter-dependent partial differential equations (PDEs). When the aim is to solve such PDEs for a large number of parameter values, Reduced Basis Methods (RBM) are often used to reduce…

The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By…

Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods…

This paper studies offline policy learning, which aims at utilizing observations collected a priori (from either fixed or adaptively evolving behavior policies) to learn an optimal individualized decision rule that achieves the best overall…

We propose techniques for approximating bilevel optimization problems with non-smooth lower level problems that can have a non-unique solution. To this end, we substitute the expression of a minimizer of the lower level minimization problem…

Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

This paper is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM) proposed in [42]. The study introduces modifications to the jumps and averages in…

Solving optimization problems is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or…

In real-world scenarios, datasets collected from randomized experiments are often constrained by size, due to limitations in time and budget. As a result, leveraging large observational datasets becomes a more attractive option for…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

Bilevel Optimization has witnessed notable progress recently with new emerging efficient algorithms and has been applied to many machine learning tasks such as data cleaning, few-shot learning, and neural architecture search. However,…

The Immersed Boundary Method (IBM) is a popular numerical approach to impose boundary conditions without relying on body-fitted grids, thus reducing the costly effort of mesh generation. To obtain enhanced accuracy, IBM can be combined with…

We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of…

Functional bilevel methods estimate a lower-level function and plug it into a hypergradient, but this plug-in gradient can retain first-order bias when the lower-level problem is learned nonparametrically. To remove this bias, we develop a…

Some recent works in machine learning and computer vision involve the solution of a bi-level optimization problem. Here the solution of a parameterized lower-level problem binds variables that appear in the objective of an upper-level…

This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR)…