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

• Published in: SIAM journal on control and optimization Vol. 37; no. 3; pp. 731 - 764
• Main Authors: Ulbrich, Michael, Ulbrich, Stefan, Heinkenschloss, Matthias
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 1999
• Subjects: Algorithms; Applied mathematics; Applied sciences; Computer science; control theory; systems; Control theory. Systems; Dimensional analysis; Exact sciences and technology; Hilbert space; Operational research and scientific management; Operational research. Management science; Optimal control; Optimization; Optimization. Search problems; Non convex programming; Optimal control; Interior point method; Non linear programming; Infinite dimension; Convergence; Constrained optimization
• ISSN: 0363-0129; 1095-7138
• DOI: 10.1137/S0363012997319541

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.