Related papers: On efficiently computing the eigenvalues of limite…
Distributed computing is critically important for modern statistical analysis. Herein, we develop a distributed quasi-Newton (DQN) framework with excellent statistical, computation, and communication efficiency. In the DQN method, no…
Some fast algorithms for computing the eigenvalues of a block companion matrix $A = U + XY^H$, where $U\in \mathbb C^{n\times n}$ is unitary block circulant and $X, Y \in\mathbb{C}^{n \times k}$, have recently appeared in the literature.…
We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schroedinger…
In this paper, we study greedy variants of quasi-Newton methods. They are based on the updating formulas from a certain subclass of the Broyden family. In particular, this subclass includes the well-known DFP, BFGS and SR1 updates. However,…
Algorithms for solving nonconvex, nonsmooth, finite-sum optimization problems are proposed and tested. In particular, the algorithms are proposed and tested in the context of an optimization problem formulation arising in semi-supervised…
Nonlinear model predictive control~(NMPC) generally requires the solution of a non-convex optimization problem at each sampling instant under strict timing constraints, based on a set of differential equations that can often be stiff and/or…
Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex…
Optimization is important in machine learning problems, and quasi-Newton methods have a reputation as the most efficient numerical schemes for smooth unconstrained optimization. In this paper, we consider the explicit superlinear…
We present a quasi-Newton method for unconstrained stochastic optimization. Most existing literature on this topic assumes a setting of stochastic optimization in which a finite sum of component functions is a reasonable approximation of an…
We consider the class of optimization problems arising from computationally intensive L1-regularized M-estimators, where the function or gradient values are very expensive to compute. A particular instance of interest is the L1-regularized…
In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors…
This work concerns the global minimization of a prescribed eigenvalue or a weighted sum of prescribed eigenvalues of a Hermitian matrix-valued function depending on its parameters analytically in a box. We describe how the analytical…
Inverse problems span across diverse fields. In medical contexts, computed tomography (CT) plays a crucial role in reconstructing a patient's internal structure, presenting challenges due to artifacts caused by inherently ill-posed inverse…
We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup with respect to the best classical…
A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…
Applications related to artificial intelligence, machine learning, and system identification simulations essentially use eigenvectors. Calculating eigenvectors for very large matrices using conventional methods is compute-intensive and…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to…
We propose a communication efficient quasi-Newton method for large-scale multi-agent convex composite optimization. We assume the setting of a network of agents that cooperatively solve a global minimization problem with strongly convex…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…