Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
On the global convergence of trust region algorithms using inexact gradient information
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Multigrid
Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations
SIAM Journal on Scientific Computing
Assessing the performance of an optimization-based multilevel method
Optimization Methods & Software - Advances in Shape and Topology Optimization: Theory, Numerics and New Applications Areas
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Many optimization algorithms require gradients of the model functions, but computing accurate gradients can be computationally expensive. We study the implications of using inexact gradients in the context of the multilevel optimization algorithm MG/Opt. MG/Opt recursively uses (typically cheaper) coarse models to obtain search directions for finer-level models. However, MG/Opt requires the gradient on the fine level to define the recursion. Our primary focus here is the impact of the gradient errors on the multilevel recursion. We analyze, partly through model problems, how MG/Opt is affected under various assumptions about the source of the error in the gradients, and demonstrate that in many cases the effect of the errors is benign. Computational experiments are included.