Related papers: Time Relaxation with Iterative Modified Lavrentiev…
Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…
This note is devoted to a simple method for proving hypocoercivity of the solutions of a kinetic equation involving a linear time relaxation operator, i.e. the construction of an adapted Lyapunov functional satisfying a Gronwall-type…
The development of finite/fixed-time stable optimization algorithms typically involves study of specific problem instances. The lack of a unified framework hinders understanding of more sophisticated algorithms, e.g., primal-dual gradient…
This paper provides a new regularization method which is particularly suitable for linear exponentially ill-posed problems. Under logarithmic source conditions (which have a natural interpretation in terms of Sobolev spaces in the…
The Scheduled Relaxation Jacobi (SRJ) method is a linear solver algorithm which greatly improves the convergence of the Jacobi iteration through the use of judiciously chosen relaxation factors (an SRJ scheme) which attenuate the solution…
We consider joint Tikhonov- and Lavrentiev-regularization of control problems with pointwise control- and state-constraints. We derive error estimates for the error which is introduced by the Tikhonov regularization. With the help of this…
The Kaczmarz method is a popular iterative method for solving consistent, overdetermined linear system such as medical imaging in computerized tomography. The Kaczmarz's iteration repeatedly scans all equations in order, which leads to…
Stabilization of linear systems with unknown dynamics is a canonical problem in adaptive control. Since the lack of knowledge of system parameters can cause it to become destabilized, an adaptive stabilization procedure is needed prior to…
This paper considers time-average optimization, where a decision vector is chosen every time step within a (possibly non-convex) set, and the goal is to minimize a convex function of the time averages subject to convex constraints on these…
In studying the time evolution of isolated many-body quantum systems, a key focus is determining whether the system undergoes relaxation and reaches a steady state at a given point in time. Traditional approaches often rely on specific…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is…
Mathematical Programs with Vanishing Constraints (MPVCs) are a notoriously challenging class of problems owing to their lack of constraint qualification. Therefore, to tackle these problems, relaxation-based approaches are typically used.…
This paper tackles forecast combination with many forecasts or minimum variance portfolio selection with many assets. A novel convex problem called L2-relaxation is proposed. In contrast to standard formulations, L2-relaxation minimizes the…
We describe a simple and flexible method for implementing semi-definite programming relaxations for bounding the set of quantum correlations. The method relies on obtaining equality constraints from randomly sampled moment matrices and…
Travel time tomography is used to infer the underlying three-dimensional wavespeed structure of the Earth by fitting seismic travel time data collected at surface stations. Data interpolation and denoising techniques are important…
We propose \textit{Meta-Regularization}, a novel approach for the adaptive choice of the learning rate in first-order gradient descent methods. Our approach modifies the objective function by adding a regularization term on the learning…
The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a…
We introduce a semidefinite relaxation for optimal control of linear systems with time scaling. These problems are inherently nonconvex, since the system dynamics involves bilinear products between the discretization time step and the…
We present a latent-space formulation of adaptive temporal lifting for continuous-time dynamical systems. The method introduces a smooth monotone mapping $t \mapsto \tau(t)$ that regularizes near-singular behavior of the underlying flow…