Friday, 15:45 - 16:10 h, Room: MA 004


William Hager
A primal-dual active set algorithm for nonlinear optimization with polyhedral constraints

Coauthor: Hongchao Zhang


A primal-dual active set algorithm is developed
for nonlinear optimization with polyhedral constraints.
The algorithm consists of a nonmonotone gradient projection
phase implemented by dual active set techniques,
an unconstrained optimization phase in the subspace
determined by the active set, and a set of rules for
branching between the two phases. Global convergence to
a stationary point is established. For a nondegenerate
stationary point, the algorithm eventually reduces to an
unconstrained optimization in a subspace without restarts.
Similarly, for a degenerate stationary point where
the strong second-order sufficient optimality
condition holds, the algorithm eventually reduces
to unconstrained optimization in a subspace. A specific
implementation of the algorithm is given which exploits
a new dual active set algorithm for the gradient projection
step and the conjugate gradient algorithm \texttt{CG\DESCENT} for
unconstrained optimization.


Talk 2 of the invited session Fri.3.MA 004
"Fast gradient methods for nonlinear optimization and applications II" [...]
Cluster 16
"Nonlinear programming" [...]


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