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Found 9 papers, 5 papers with code
Registration of algebraic varieties using Riemannian optimization
Our approach is particularly useful when the two point clouds describe different parts of an objects (which may not even be overlapping), on the condition that the surface of the object may be well approximated by a set of polynomial equations.
A Randomised Subspace Gauss-Newton Method for Nonlinear Least-Squares
We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on each iteration.
Nonlinear matrix recovery using optimization on the Grassmann manifold
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.
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, $m=\mathcal{O}(d)$, where $d$ is the dimension of the subspace.
Scalable Derivative-Free Optimization for Nonlinear Least-Squares Problems
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.
Escaping local minima with derivative-free methods: a numerical investigation
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
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
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
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
