相关论文: A variable dimension sketching strategy for nonlin…

This paper addresses the challenge of solving large-scale nonlinear equations with H\"older continuous Jacobians. We introduce a novel Incremental Gauss--Newton (IGN) method within explicit superlinear convergence rate, which outperforms…

For large nonlinear least squares loss functions in machine learning we exploit the property that the number of model parameters typically exceeds the data in one batch. This implies a low-rank structure in the Hessian of the loss, which…

We consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions…

We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…

We study nonlinear constrained optimization problems in which only function evaluations of the objective and constraints are available. Existing zeroth-order methods rely on noisy gradient and Jacobian surrogates in high dimensions, making…

The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…

This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

Matrix sketching is a powerful tool for reducing the size of large data matrices. Yet there are fundamental limitations to this size reduction when we want to recover an accurate estimator for a task such as least square regression. We show…

We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…

We present DFO-GN, a derivative-free version of the Gauss-Newton method for solving nonlinear least-squares problems. As is common in derivative-free optimization, DFO-GN uses interpolation of function values to build a model of the…

A numerical method optimizing the coefficients of the semi empirical mass formula or those of similar mass formulas is presented. The optimization is based on the least-squares adjustments method and leads to the resolution of a linear…

In this work, we establish non-asymptotic convergence bounds for the Gauss-Newton method in training neural networks with smooth activations. In the underparameterized regime, the Gauss-Newton gradient flow in parameter space induces a…

For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…

We propose a novel stochastic gradient descent method for solving linear least squares problems with partially observed data. Our method uses submatrices indexed by a randomly selected pair of row and column index sets to update the iterate…

Classical theory for quasi-Newton schemes has focused on smooth deterministic unconstrained optimization while recent forays into stochastic convex optimization have largely resided in smooth, unconstrained, and strongly convex regimes.…

A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…

Based on differences of points and differences of gradients over the most recent three iterations, together with the Taylor's theorem, two forms of the quasi-Newton equations at the recent iteration are constructed. By using the two forms…

We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…

Gauss-Newton methods and their stochastic version have been widely used in machine learning and signal processing. Their nonsmooth counterparts, modified Gauss-Newton or prox-linear algorithms, can lead to contrasting outcomes when compared…