Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton’s method for solving finite-sum optimization problems in which the number of variables and data points are both large. We study two forms of sketching that perform dimensionality reduction in data space: … Read more
This paper proposes two proximal Newton-CG methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a a reformulation of the original nonsmooth problem as the unconstrained minimization of a continuously differentiable function, namely the forward-backward envelope (FBE). The first algorithm is based on a standard line search strategy, whereas the … Read more
In a recent paper by Monteiro and Svaiter, a hybrid proximal extragradient framework has been used to study the iteration-complexity of a first-order (or, in the context of optimization, second-order) method for solving monotone nonlinear equations. The purpose of this paper is to extend this analysis to study a prox-type first-order method for monotone smooth … Read more
We focus on the numerical solution of medium scale bound-constrained systems of nonlinear equations. In this context, we consider an affine-scaling trust region approach that allows a great flexibility in choosing the scaling matrix used to handle the bounds. The method is based on a dogleg procedure tailored for constrained problems and so, it is … Read more
This thesis is about mathematical optimization. Mathematical optimization involves the construction of methods to solve optimization problems, which can arise from real-life problems in applied science, when they are mathematically modeled. Examples come from electrical design, engineering, control theory, telecommunication, environment, finance, and logistics. This thesis deals especially with semidefinite optimization problems. Semidefinite programming is … Read more