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Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
Optimal control synthesis in stochastic systems with respect to quantitative temporal logic constraints can be formulated as linear programming problems. However, centralized synthesis algorithms do not scale to many practical systems. To…
We propose a new methodology for parameterized constrained robust optimization, an important class of optimization problems under uncertainty, based on learning with a self-supervised penalty-based loss function. Whereas supervised learning…
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…
We have recently presented a method to solve an overdetermined linear system of equations with multiple right hand side vectors, where the unknown matrix is to be symmetric and positive definite. The coefficient and the right hand side…
This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…
Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…
In this paper, we investigate the problem of unified prescribed performance tracking for a class of non-square strict-feedback nonlinear systems under relaxed controllability conditions. By using a skillful matrix decomposition and…
This paper proposes novel approaches for designing control Lyapunov functions (CLFs) for constrained linear systems. We leverage recent configuration-constrained polyhedral computing techniques to devise piecewise affine convex CLFs.…
Many computational problems involve optimization over discrete variables with quadratic interactions. Known as discrete quadratic models (DQMs), these problems in general are NP-hard. Accordingly, there is increasing interest in encoding…
A $\mathcal{H}_2$-guaranteed sparse-feedback linear-quadratic (LQ) optimal control with convex parameterization and convex-bounded uncertainty is studied in this paper, where $\ell_0$-penalty is added into the $\mathcal{H}_2$ cost to…
This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state…
This survey explores the geometric perspective on policy optimization within the realm of feedback control systems, emphasizing the intrinsic relationship between control design and optimization. By adopting a geometric viewpoint, we aim to…
In this paper, we introduce a significant extension, called scenario with certificates (SwC), of the so-called scenario approach for uncertain optimization problems. This extension is motivated by the observation that in many control…
In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
In Constrained Reinforcement Learning (CRL), agents explore the environment to learn the optimal policy while satisfying constraints. The penalty function method has recently been studied as an effective approach for handling constraints,…
In this article, we investigate the multi-parametric matroid problem. The weights of the elements of the matroid's ground set depend linearly on an arbitrary but fixed number of parameters, each of which is taken from a real interval. The…
In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for solving elliptic PDE-constrained optimization or optimal…