Related papers: Shifted L-BFGS Systems
Motivated by applications arising from large scale optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving unconstrained convex optimization problems. The convergence analysis of the SQN methods,…
Backward Filtering Forward Guiding (BFFG) is a bidirectional algorithm proposed in Mider et al. [2021] and studied more in depth in a general setting in Van der Meulen and Schauer [2022]. In category theory, optics have been proposed for…
We consider the problem of attaining either the maximal increase or reduction of the robustness of a complex network by means of a bounded modification of a subset of the edge weights. We propose two novel strategies combining Krylov…
Recommendation from implicit feedback is a highly challenging task due to the lack of the reliable observed negative data. A popular and effective approach for implicit recommendation is to treat unobserved data as negative but downweight…
This paper focuses studies the following low rank + sparse (LR+S) column-wise compressive sensing problem. We aim to recover an $n \times q$ matrix, $\X^* =[ \x_1^*, \x_2^*, \cdots , \x_q^*]$ from $m$ independent linear projections of each…
We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
A method is presented to obtain an inner-approximation of the backward reachable set (BRS) of a given target tube, along with an admissible controller that maintains trajectories inside this tube. The proposed optimization algorithms are…
We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the…
Recent advances in machine learning, specifically transformer architecture, have led to significant advancements in commercial domains. These powerful models have demonstrated superior capability to learn complex relationships and often…
We consider systems of linear differential and difference equations \begin{eqnarray*} \partial Y(x) =A(x)Y(x), \sigma Y(x) =B(x)Y(x) \end{eqnarray*} with $\partial = \frac{d}{dx}$, $\sigma$ a shift operator $\sigma(x) = x+a$, $q$-dilation…
B* is a novel optimization framework that addresses a critical challenge in fixed-base manipulator robotics: optimal base placement. Current methods rely on pre-computed kinematics databases generated through sampling to search for…
In this work, we study optimization problems of the form $\min_x \max_y f(x, y)$, where $f(x, y)$ is defined on a product Riemannian manifold $\mathcal{M} \times \mathcal{N}$ and is $\mu_x$-strongly geodesically convex (g-convex) in $x$ and…
The $G^{+}$ method is a new method, a powerful one, for the study of (homogeneous and nonhomogeneous) products of nonnegative matrices -- for problems on the products of nonnegative matrices. To study such products, new classes of matrices…
Flexible systems are linear systems of inclusions in which the elements of the coefficient matrix are external numbers in the sense of nonstandard analysis. External numbers represent real numbers with small, individual error terms. Using…
We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…
Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…
We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…
We propose a new way for speeding up the search of the maximal solution $X_+$ of $X + A^\top X^{-1} A = Q$. It is known that the speed of convergence of traditional approaches for solving this problem depends highly on the spectral radius…
The Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…