David Torregrosa-Belén

Randomized block proximal method with locally Lipschitz continuous gradient

Categories Nonlinear Optimization Tags , , , ,

Block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails substantial memory requirements and computational efforts. In this paper, we propose a randomized block proximal gradient algorithm for minimizing the sum of a smooth function and a separable proper lower semicontinuous function, both possibly … Read more

A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Łojasiewicz condition

Categories Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function. We target a broad class of integrands obeying a nonsmooth, localized variant of the descent lemma in the decision variable, a structural assumption that simultaneously covers … Read more

Optimal diagonal preconditioning beyond worst-case conditioning: theory and practice of omega scaling

Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization, Optimization in Data Science Tags , , , ,

Preconditioning is essential in many areas of mathematics, and in particular is a fundamental tool for accelerating iterative methods for solving linear systems. In this work, we study optimal diagonal preconditioning under two distinct notions of conditioning: the classical worst-case \(\kappa\)-condition number and the averaging-based \(\omega\)-condition number. We observe that \(\omega\)-optimal preconditioning generally outperforms \(\kappa\)-optimal … Read more

Approaches to iterative algorithms for solving nonlinear equations with an application in tomographic absorption spectroscopy

Categories Biomedical Applications, Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , , ,

In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with variables coupling, we consider a situation where straightforward translation to a fixed point problem is not possible because the operators that represent the … Read more

Preconditioning for Generelized Jacobians with the ω-Condition Number

Categories Nonsmooth Optimization, Other Topics Tags , , ,

Preconditioning is essential in iterative methods for solving linear systems of equations. We study a nonclassic matrix condition number, the ω-condition number, in the context of optimal conditioning for low rank updating of positive definite matrices. For a positive definite matrix, this condition measure is the ratio of the arithmetic and geometric means of the … Read more

The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , ,

In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced … Read more