## Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training

A class of multi-level algorithms for unconstrained nonlinear optimization is presented which does not require the evaluation of the objective function. The class contains the momentum-less AdaGrad method as a particular (single-level) instance. The choice of avoiding the evaluation of the objective function is intended to make the algorithms of the class less sensitive to … Read more

## A classification method based on a cloud of spheres

 In this article we propose a binary classification model to distinguish a specific class that corresponds to a characteristic that we intend to identify (fraud, spam, disease). The classification model is based on a cloud of spheres that circumscribe the points of the class to be identified. It is intended to build a model … Read more

## A Levenberg-Marquardt Method for Nonsmooth Regularized Least Squares

 We develop a Levenberg-Marquardt method for minimizing the sum of a smooth nonlinear least-squares term $$f(x) = \frac{1}{2} \|F(x)\|_2^2$$ and a nonsmooth term $$h$$. Both $$f$$ and $$h$$ may be nonconvex. Steps are computed by minimizing the sum of a regularized linear least-squares model and a model of $$h$$ using a first-order method such … Read more

## Inexact Proximal-Gradient Methods with Support Identification

 We consider the proximal-gradient method for minimizing an objective function that is the sum of a smooth function and a non-smooth convex function. A feature that distinguishes our work from most in the literature is that we assume that the associated proximal operator does not admit a closed-form solution. To address this challenge, we … Read more

## Stochastic nested primal-dual method for nonconvex constrained composition optimization

In this paper we study the nonconvex constrained composition optimization, in which the objective contains a composition of two expected-value functions whose accurate information is normally expensive to calculate. We propose a STochastic nEsted Primal-dual (STEP) method for such problems. In each iteration, with an auxiliary variable introduced to track inner layer function values we … Read more