pseudoconvex function

New insights and algorithms for optimal diagonal preconditioning

  • 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 (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

    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