Global Convergence of Trust-region Interior-point Algorithms for Infinite-dimensional Nonconvex Minimization Subject to Pointwise Bounds

Authors:
Michael Ulbrich;Stefan Ulbrich;Matthias Heinkenschloss
Affiliations:
-;-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1999

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Abstract

A class of interior-point trust-region algorithms for infinite-dimensional nonlinear optimization subject to pointwise bounds in L p-Banach spaces, $2\le p\le\infty$, 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.