Related papers: Iterative Hessian sketch: Fast and accurate soluti…
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
This paper proposes a novel Hessian approximation for Maximum a Posteriori estimation problems in robotics involving Gaussian mixture likelihoods. Previous approaches manipulate the Gaussian mixture likelihood into a form that allows the…
Motivated by recent advances in serverless cloud computing, in particular the "function as a service" (FaaS) model, we consider the problem of minimizing a convex function in a massively parallel fashion, where communication between workers…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
We propose a regularized Hessian-free Newton-type method for minimizing smooth convex functions with Lipschitz continuous Hessians. The algorithm constructs an approximate Hessian by finite differences and selects the regularization…
The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel…
We consider a sketched implementation of the finite element method for elliptic partial differential equations on high-dimensional models. Motivated by applications in real-time simulation and prediction we propose an algorithm that…
High-dimensional representations, such as radial basis function networks or tile coding, are common choices for policy evaluation in reinforcement learning. Learning with such high-dimensional representations, however, can be expensive,…
We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a low-dimensional subspace of operators by solving a small…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
Clinically useful proton Computed Tomography images will rely on algorithms to find the three-dimensional proton stopping power distribution that optimally fits the measured proton data. We present a least squares iterative method with many…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Researchers may perform regressions using a sketch of data of size $m$ instead of the full sample of size $n$ for a variety of reasons. This paper considers the case when the regression errors do not have constant variance and…
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…
In many applications of tomography, the acquired projections are either limited in number or contain a significant amount of noise. In these cases, standard reconstruction methods tend to produce artifacts that can make further analysis…
The method of ``Total Least Squares'' is proposed as a more natural way (than ordinary least squares) to approximate the data if both the matrix and and the right-hand side are contaminated by ``errors''. In this tutorial note, we give a…
Quasi-Newton (QN) methods provide an efficient alternative to second-order methods for minimizing smooth unconstrained problems. While QN methods generally compose a Hessian estimate based on one secant interpolation per iteration,…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…