Pedro Pérez-Aros (Universidad de O'Higgins, Rancagua)
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  In this presentation, we explore a new category of challenging nonsmooth
  optimization problems. These problems involve the difference between generally
  nonconvex functions as their objective. We introduce an innovative Newton-type
  algorithm designed for solving such problems. This algorithm leverages
  advanced tools from variational analysis and is based on the concept of the
  coderivative generated second-order subdifferential (generalized Hessian). We
  discuss the algorithm's well-posedness properties, establishing its viability
  under broad conditions. Additionally, we analyze its convergence rates,
  incorporating assumptions such as the Kurdyka–Łojasiewicz condition. The talk
  ends with  some numerical experiments which ilustrate the performance of our
  development.