Superlinear convergence of affine-scaling interior-point Newton methods for infinite-dimensional nonlinear problems with pointwise bounds

SIAM Journal on Control and Optimization

Volumn 38, Issue 6, 2000, Pages 1938-1984

  Ulbrich, Michael ^a   Ulbrich, Stefan ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; NONLINEAR PROGRAMMING; OPTIMAL CONTROL SYSTEMS;

INTERIOR-POINT ALGORITHMS; NEWTON METHOD;

CONTROL SYSTEM ANALYSIS;

EID: 0034544017     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012997325915     Document Type: Article

References (28)

1. R. ADAMS, Sobolev Spaces, Academic Press, New York, 1975.
2. W. ALT, The Lagrange-Newton method for infinite dimensional optimization problems, Numer. Funct. Anal. Optim., 11 (1990), pp. 201-224.
3. D. P. BERTSEKAS, Projected Newton methods for optimization problems with simple constraints, SIAM J. Control Optim., 20 (1982), pp. 221-246.
4. M. A. BRANCH, T. F. COLEMAN, AND Y. LI, A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems, Tech. Rep. CTC95TR217, Center for Theory and Simulation in Science and Engineering, Cornell University, Ithaca, NY, 1995.
5. J. BURGER AND M. POGU, Functional and numerical solution of a control problem originating from heat transfer, J. Optim. Theory Appl., 68 (1991), pp. 49-73.
6. T. F. COLEMAN AND Y. LI, On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds, Math. Programming, 67 (1994), pp. 189-224.
7. T. F. COLEMAN AND Y. LI, An interior trust region approach for nonlinear minimization subject to bounds, SIAM J. Optim., 6 (1996), pp. 418-445.
8. J. E. DENNIS, M. HEINKENSCHLOSS, AND L. N. VICENTE, Trust-region interior-point SQP algorithms for a class of nonlinear programming problems, SIAM J. Control Optim., 36 (1998), pp. 1750-1794.
9. J. C. DUNN AND T. TIAN, Variants of the Kuhn-Tucker sufficient conditions in cones of nonnegative functions, SIAM J. Control Optim., 30 (1992), pp. 1361-1384.
10. ∞ functions with range in a polyhedron, SIAM J. Control Optim., 33 (1995), pp. 1603-1635.
11. 2-sufficient conditions and the gradient projection method for optimal control problems, SIAM J. Control Optim., 34 (1996), pp. 1270-1290.
12. A. GRIEWANK, The local convergence of Broyden-like methods on, Lipschitzian problems in Hilbert spaces, SIAM J. Numer. Anal., 24 (1987), pp. 684-705.
13. M. HEINKENSCHLOSS, A trust region method for norm constrained problems, SIAM J. Numer. Anal., 35 (1998), pp. 1594-1620.
14. M. HEINKENSCHLOSS, Projected sequential quadratic programming methods, SIAM J. Optim., 6 (1996), pp. 373-417.
15. M. HEINKENSCHLOSS AND L. N. VICENTE, Analysis of Inexact Trust-Region Interior-Point SQP Algorithms, Tech. Rep. TR95-18, Department of Computational and Applied Mathematics, Rice University, Houston, TX, 1995.
16. C. T. KELLEY AND E. W. SACHS, Quasi-Newton methods and unconstrained optimal control problems, SIAM J. Control Optim., 25 (1987), pp. 1503-1516.
17. C. T. KELLEY AND E. W. SACHS, Multilevel algorithms for constrained compact fixed point problems, SIAM J. Sci. Comput., 15 (1994), pp. 645-667.
18. C. T. KELLEY AND E. W. SACHS, Solution of optimal control problems by a pointwise projected Newton method, SIAM J. Control Optim., 33 (1995), pp. 1731-1757.
19. C. T. KELLEY AND E. W. SACHS, A Trust Region Method for Parabolic Boundary Control Problems, Tech. Rep. CRSC-TR96-28, Center for Research in Scientific Computing, North Carolina State University, Raleigh, NC, 1996.
20. F.-S. KUPFER AND E. W. SACHS, Numerical solution of a nonlinear parabolic control problem by a reduced SQP method, Comput. Optim. Appl., 1 (1992), pp. 113-135.
21. J. L. LIONS, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris, 1969.
22. J. L. LIONS, Optimal Control of Systems Governed by Partial Differential Equations, Springer, New York, 1971.
23. H. MAURER, First and second order sufficient optimality conditions in mathematical programming and optimal control, Math. Programming Stud., 14 (1981), pp. 163-177.
24. E. SACHS, A parabolic control problem with a boundary condition of the Stefan-Boltzmann type, Z. Angew. Math. Mech., 58 (1978), pp. 443-449.
25. 2 inputs, SIAM J. Control Optim., 32 (1994), pp. 516-537.
26. M. ULBRICH, S. ULBRICH, AND M. HEINKENSCHLOSS, Global convergence of trust-region interior-point algorithms for infinite-dimensional nonconvex minimization subject to pointwise bounds, SIAM J. Control Optim., 37 (1999), pp. 731-764.
27. L. N. VICENTE, Trust-Region Interior-Point Algorithms for a Class of Nonlinear Programming Problems, Ph.D. thesis, Department of Computational and Applied Mathematics, Rice University, Houston, TX, 1996.
28. L. N. VICENTE, On interior-point Newton algorithms for discretized optimal control problems with state constraints, Optim. Methods Softw., 8 (1998), pp. 249-275.