local quadratic convergence

Local Convergence Analysis of an Inexact Trust-Region Method for Nonsmooth Optimization

  • Robert Baraldi
  • Drew P. Kouri
    • Categories Infinite Dimensional Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1–40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function in Hilbert space—a class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. This algorithm has demonstrated … Read more

    A New Error Bound Result for Generalized Nash Equilibrium Problems and its Algorithmic Application

  • Axel Dreves
  • Francisco Facchinei
  • Andreas Fischer
  • Markus Herrich
    • Categories Complementarity and Variational Inequalities, Game Theory, Nonlinear Optimization Tags , , , , ,

    We present a new algorithm for the solution of Generalized Nash Equilibrium Problems. This hybrid method combines the robustness of a potential reduction algorithm and the local quadratic convergence rate of the LP-Newton method. We base our local convergence theory on an error bound and provide a new sufficient condition for it to hold that … Read more