Dimitri Tomanos

Numerical Experience with a Recursive Trust-Region Method for Multilevel Nonlinear Optimization

  • Serge Gratton
  • Annick Sartenaer
  • Philippe L. Toint
  • Mélodie Mouffe
  • Dimitri Tomanos
    • Categories Bound-constrained Optimization, Distributed Control, Optimization of Systems modeled by PDEs Tags , , , , ,

    We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton, Mouffe, Toint, Weber (2008) for bound-constrained nonlinear problems, and provide numerical experience on multilevel test problems. A suitable choice of the algorithm’s parameters is identified on these problems, yielding a satisfactory compromise between reliability and efficiency. The resulting default algorithm is then … Read more

    A Retrospective Trust-Region Method for Unconstrained Optimization

  • Fabian Bastin
  • Vincent Malmedy
  • Philippe L. Toint
  • Mélodie Mouffe
  • Dimitri Tomanos
    • Categories Unconstrained Optimization Tags , , ,

    We introduce a new trust-region method for unconstrained optimization where the radius update is computed using the model information at the current iterate rather than at the preceding one. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at last iterate. Global convergence to … Read more

    A multilevel algorithm for solving the trust-region subproblem

  • Philippe L. Toint
  • Melissa Weber-Mendonca
  • Dimitri Tomanos
    • Categories Infinite Dimensional Optimization, Optimization of Systems modeled by PDEs, Unconstrained Optimization Tags , , ,

    We present a multilevel numerical algorithm for the exact solution of the Euclidean trust-region subproblem. This particular subproblem typically arises when optimizing a nonlinear (possibly non-convex) objective function whose variables are discretized continuous functions, in which case the different levels of discretization provide a natural multilevel context. The trust-region problem is considered at the highest … Read more