Global Convergence of Trust-Region Interior-Point
Algorithms for Infinite-Dimensional Nonconvex
Minimization Subject to Pointwise Bounds
Michael Ulbrich
Technische Universität München
Institut für Angewandte Mathematik und Statistik
Stefan Ulbrich
Technische Universität München
Institut für Angewandte Mathematik und Statistik
Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
SIAM J. Control and Optimization, Vol. 37, 1999, pages 731-764.
Abstract
A class of interior-point trust-region algorithms for
infinite-dimensional nonlinear optimization subject to
pointwise bounds in L^p-Banach spaces, 2 <= p <= infinity,
is formulated and analyzed. The problem formulation is
motivated by optimal control problems with L^p-controls
and pointwise control constraints.
The interior-point trust-region algorithms are generalizations
of those recently introduced by Coleman and Li
(SIAM J. Optim., 6 (1996), pp. 418-445) for finite-dimensional
problems.
Many of the generalizations derived in this paper are also important
in the finite dimensional context.
All first- and second-order global convergence results known
for trust-region methods in the finite-dimensional setting are extended
to the infinite-dimensional framework of this paper.
Keywords
Infinite-dimensional optimization, bound constraints
affine scaling, interior-point algorithms,
trust-region methods, global convergence,
optimal control, nonlinear programming.
1991 Mathematics Subject Classification
49M37, 65K05, 90C30, 90C48.
See also the follow-up paper
M. Ulbrich and S. Ulbrich:
Superlinear convergence of affine-scaling
interior-point Newton methods for infinite-dimensional nonlinear problems
with pointwise bounds.