| Abstract |
In this talk, 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 true multilevel/multiscale optimization methods
reminiscent of multigrid methods in linear algebra and the solution of
partial-differential equations. First and second-order convergence
properties of this class of algorithms will be outlined and preliminary
numerical experience will be described on a small set of multiscale
nonlinear optimization problems.
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