Adjoint-based Quasi-Newton Methods for Nonlinear Equations
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Beschreibung
In this thesis a new class of rank-1 update formulas
is investigated. It is applied to approximate
Jacobians in quasi-Newton methods for the solution
of nonlinear equations. The update formulas
make explicite use of adjoint and partly direct derivative
information. For example, these derivatives
can be efficiently evaluated by methods of
Automatic Differentiation.
A particular feature of the update formulas is that
they combine the fixed scale least change property
of Broyden’s update with the heredity property of
the SR1 update. This allows to prove rapid local
superlinear convergence. Moreover, in combination
with line search, global convergence results are
established. The new quasi-Newton methods are
applied to various test problems and compared to
other well established methods.
Autor*in
Sebastian Schlenkrich
Themen in »Adjoint-based Quasi-Newton Methods for Nonlinear Equations«
Nonlinear Equations QR-factorizations Quasi-Newton Methods