Serge Gratton

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

  • Serge Gratton
  • Annick Sartenaer
  • Philippe L. Toint
    • Categories Nonlinear Optimization, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , , , ,

    We consider an implementation of the recursive multilevel trust-region algorithm proposed by Gratton, Sartenaer, Toint (2004), and provide significant numerical experience on multilevel test problems. A suitable choice of the algorithm’s parameters is identified on these problems, yielding a very satisfactory compromise between reliability and efficiency. The resulting default algorithm is then compared to alternative … Read more

    Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization

  • Serge Gratton
  • Annick Sartenaer
  • Philippe L. Toint
    • Categories Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , ,

    Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function’s local curvature is incomplete, in the sense that it may be restricted to a fixed set of “test directions” and may not be available at every iteration. It is shown that convergence to local “weak” … Read more

    Recursive Trust-Region Methods for Multilevel Nonlinear Optimization (Part I): Global Convergence and Complexity

  • Serge Gratton
  • Annick Sartenaer
  • Philippe L. Toint
    • Categories Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , , , ,

    A class of trust-region methods is presented for solving unconstrained nonlinear and possibly nonconvex discretized optimization problems, like those arising in systems governed by partial differential equations. The algorithms in this class make use of the discretization level as a mean of speeding up the computation of the step. This use is recursive, leading to … Read more