Search Results for author: Coralia Cartis

Found 7 papers, 4 papers with code

Nonlinear matrix recovery using optimization on the Grassmann manifold

1 code implementation13 Sep 2021 Florentin Goyens, Coralia Cartis, Armin Eftekhari

We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters.

Riemannian optimization

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

no code implementations25 May 2021 Coralia Cartis, Jan Fiala, Zhen Shao

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, $m=\mathcal{O}(d)$, where $d$ is the dimension of the subspace.

Scalable Derivative-Free Optimization for Nonlinear Least-Squares Problems

no code implementations26 Jul 2020 Coralia Cartis, Tyler Ferguson, Lindon Roberts

Derivative-free - or zeroth-order - optimization (DFO) has gained recent attention for its ability to solve problems in a variety of application areas, including machine learning, particularly involving objectives which are stochastic and/or expensive to compute.

Dimensionality Reduction

Escaping local minima with derivative-free methods: a numerical investigation

1 code implementation29 Dec 2018 Coralia Cartis, Lindon Roberts, Oliver Sheridan-Methven

We apply a state-of-the-art, local derivative-free solver, Py-BOBYQA, to global optimization problems, and propose an algorithmic improvement that is beneficial in this context.

Optimization and Control

Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints

no code implementations3 Nov 2018 Coralia Cartis, Nick I. M. Gould, Philippe L. Toint

We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i. e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected) constraints, if any, is negligible compared to that of evaluating the objective function.

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

3 code implementations31 Mar 2018 Coralia Cartis, Jan Fiala, Benjamin Marteau, Lindon Roberts

Numerical results show DFO-LS can gain reasonable progress on some medium-scale problems with fewer objective evaluations than is needed for one gradient evaluation.

Optimization and Control

Active-set prediction for interior point methods using controlled perturbations

1 code implementation27 Apr 2014 Coralia Cartis, Yiming Yan

We also find that a primal-dual path-following algorithm applied to the perturbed problem is able to accurately predict the optimal active set of the original problem when the duality gap for the perturbed problem is not too small; furthermore, depending on problem conditioning, this prediction can happen sooner than predicting the active set for the perturbed problem or when the original one is solved.

Optimization and Control

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