Andrea Brilli

Nonlinear Derivative-free Constrained Optimization with a Mixed Penalty-Logarithmic Barrier Approach and Direct Search

  • Andrea Brilli
  • Ana Luisa Custódio
  • Giampaolo Liuzzi
  • Everton Silva
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In this work, we propose the joint use of a mixed penalty-logarithmic barrier approach and generating set search, for addressing nonlinearly constrained derivative-free optimization problems. A merit function is considered, wherein the set of inequality constraints is divided into two groups: one treated with a logarithmic barrier approach, and another, along with the equality constraints, … Read more

    Complexity results and active-set identification of a derivative-free method for bound-constrained problems

  • Andrea Brilli
  • Andrea Cristofari
  • Giampaolo Liuzzi
  • Stefano Lucidi
    • Categories Bound-constrained Optimization, Nonlinear Optimization Tags , ,

    In this paper, we analyze a derivative-free line search method designed for bound-constrained problems. Our analysis demonstrates that this method exhibits a worst-case complexity comparable to other derivative-free methods for unconstrained and linearly constrained problems. In particular, when minimizing a function with $n$ variables, we prove that at most ${\cal O}(n\epsilon^{-2})$ iterations are needed to … Read more