CRPC-TR97692							March 1997

Title: Global Convergence of Trust-Region Interior-Point Algorithms for 
Infinite-Dimensional Nonconvex Minimization Subject to Pointwise Bounds

Authors: Michael Ulbrich, Stefan Ulbrich, Matthias Heinkenschloss

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. They lead to 
a better understanding of the method and to considerable improvements in 
their performance. 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.

Key Words: Infinite-dimensional optimization, bound constraints, affine 
	scaling, interior-point algorithms, trust-region methods, global 
	convergence, optimal control, nonlinear programming

AMS Subject Classifications: 49M37, 65K05, 90C30, 90C48