o-minimal structure

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

    Generic identifiability and second-order sufficiency in tame convex optimization

  • Jérôme Bolte
  • Aris Daniilidis
  • Adrian Lewis
    • Categories Convex Optimization Tags , , ,

    We consider linear optimization over a fixed compact convex feasible region that is semi-algebraic (or, more generally, “tame”). Generically, we prove that the optimal solution is unique and lies on a unique manifold, around which the feasible region is “partly smooth”, ensuring finite identification of the manifold by many optimization algorithms. Furthermore, second-order optimality conditions … Read more