Related papers: $\mathcal{H}_2$-Optimal Model Reduction Using Proj…
We consider a generic empirical composition optimization problem, where there are empirical averages present both outside and inside nonlinear loss functions. Such a problem is of interest in various machine learning applications, and…
We consider the random-design least-squares regression problem within the reproducing kernel Hilbert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function…
This paper presents the first optimal-rate $p$-th order methods with $p\geq 1$ for finding first and second-order stationary points of non-convex smooth objective functions over Riemannian manifolds. In contrast to the geodesically convex…
We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…
The finite element method is an indispensable tool in engineering, but its computational complexity prevents applications for control or at system-level. Model order reduction bridges this gap, creating highly efficient yet accurate…
Linear time-periodic (LTP) dynamical systems frequently appear in the modeling of phenomena related to fluid dynamics, electronic circuits, and structural mechanics via linearization centered around known periodic orbits of nonlinear…
Two new hybrid algorithms are proposed for large-scale linear discrete ill-posed problems in general-form regularization. They are both based on Krylov subspace inner-outer iterative algorithms. At each iteration, they need to solve a…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable…
This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art…
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…
We propose a new algorithm for the problem of recovering data that adheres to multiple, heterogeneous low-dimensional structures from linear observations. Focusing on data matrices that are simultaneously row-sparse and low-rank, we propose…
Standard H2 optimal control of networked dynamic systems tend to become unscalable with network size. Structural constraints can be imposed on the design to counteract this problem albeit at the risk of making the solution non-convex. In…
In statistics, it is common to encounter multi-modal and non-smooth likelihood (or objective function) maximization problems, where the parameters have known upper and lower bounds. This paper proposes a novel derivative-free global…
This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…
Krylov subspace recycling is a powerful tool for solving long series of large, sparse linear systems that change slowly. In PDE constrained shape optimization, these appear naturally, as hundreds or more optimization steps are needed with…
Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined components: one-dimensional linear optimization one…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
We introduce highly efficient online nonlinear regression algorithms that are suitable for real life applications. We process the data in a truly online manner such that no storage is needed, i.e., the data is discarded after being used.…
Constrained least squares problems arise in a variety of applications, and many iterative methods are already available to compute their solutions. This paper proposes a new efficient approach to solve nonnegative linear least squares…
The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…