pseudoconvex function

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

  • Saeed Ghadimi
  • Woosuk L. Jung
  • Arnesh Sujanani
  • David Torregrosa-BelĂ©n
  • Henry Wolkowicz
    • 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

    Weakly Homogeneous Optimization Problems

  • Vu Trung Hieu
    • Categories Nonlinear Optimization Tags , , , , , ,

    This paper investigates a new class of optimization problems whose objective functions are weakly homogeneous relative to the constrain sets. Two sufficient conditions for nonemptiness and boundedness of solution sets are established. We also study linear parametric problems and upper semincontinuity of the solution map. ArticleDownload View PDF