Hashing embeddings of optimal dimension, with applications to linear least squares

The aim of this paper is two-fold: firstly, to present subspace embedding properties for s-hashing sketching matrices, with $s\geq 1$, that are optimal in the projection dimension $m$ of the sketch, namely, $m=O(d)$, where $d$ is the dimension of the subspace. A diverse set of results are presented that address the case when the input … Read more

Improving the Flexibility and Robustness of Model-Based Derivative-Free Optimization Solvers

We present DFO-LS, a software package for derivative-free optimization (DFO) for nonlinear Least-Squares (LS) problems, with optional bound constraints. Inspired by the Gauss-Newton method, DFO-LS constructs simplified linear regression models for the residuals. DFO-LS allows flexible initialization for expensive problems, whereby it can begin making progress from as few as two objective evaluations. Numerical results … Read more