regular variation and Karamata theory

Concrete convergence rates for common fixed point problems under Karamata regularity

  • Tianxiang Liu
  • Bruno F. Lourenço
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    \(\) We introduce the notion of Karamata regular operators, which is a notion of regularity that is suitable for obtaining concrete convergence rates for common fixed point problems. This provides a broad framework that includes, but goes beyond, Hölderian error bounds and Hölder regular operators. By concrete, we mean that the rates we obtain are … Read more

    Convergence analysis under consistent error bounds

  • Tianxiang Liu
  • Bruno F. Lourenço
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical Lipschitzian and Holderian error bounds and includes logarithmic and entropic error bound found in the exponential cone. It also includes the error bounds obtainable under the theory of … Read more