A multilevel variational method for Au= Bu on composite Grids
Journal of Computational Physics
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Trust-region methods
Multigrid
Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations
SIAM Journal on Scientific Computing
Recursive Trust-Region Methods for Multiscale Nonlinear Optimization
SIAM Journal on Optimization
A general framework for nonlinear multigrid inversion
IEEE Transactions on Image Processing
Lagrangian Duality and Branch-and-Bound Algorithms for Optimal Power Flow
Operations Research
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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 level (corresponding to the finest discretization), but information on the problem curvature at lower levels is exploited for improved efficiency. The algorithm is inspired by the method described in [J.J. More and D.C. Sorensen, On the use of directions of negative curvature in a modified Newton method, Math. Program. 16(1) (1979), pp. 1-20], for which two different multilevel variants will be analysed. Some preliminary numerical comparisons are also presented.