David Torregrosa-Belén

New insights and algorithms for optimal diagonal preconditioning

  • Saeed Ghadimi
  • Woosuk L. Jung
  • Arnesh Sujanani
  • David Torregrosa-Belén
  • Henry Wolkowicz
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization, Optimization in Data Science Tags , , , ,

    Preconditioning (scaling) is essential in many areas of mathematics, and in particular in optimization. In this work, we study the problem of finding an optimal diagonal preconditioner. We focus on minimizing two different notions of condition number: the classical, worst-case type, \(\kappa\)-condition number, and the more averaging motivated \(\omega\)-condition number. We provide affine based pseudoconvex … Read more

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

  • Francisco J. Aragón Artacho
  • Weiwei Cai
  • Yair Censor
  • Aviv Gibali
  • Chongyuan Shui
  • David Torregrosa-Belén
    • 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

  • Woosuk L. Jung
  • David Torregrosa-Belén
  • Henry Wolkowicz
    • 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

  • Francisco J. Aragón Artacho
  • Yair Censor
  • Aviv Gibali
  • David Torregrosa-Belén
    • 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