In the age of e-commerce, many logistic companies must operate in large road networks without accurate knowledge of travel times for their specific fleet of vehicles. Moreover, millions of dollars are spent on routing services that do not accurately capture the specific characteristics of the companies’ drivers and the types of vehicles they must use. … Read more
Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a subset of points. Furthermore, this subset can be non-representative, e.g., due to self-selection in a survey. Semi-supervised SVMs tackle … Read more
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
\(\) 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 circumscribes the points of the class to be identified. It is intended to build a model … Read more
\(\) 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
\(\) 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
\(\) 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 the inner layer function … Read more