An inexact Newton method for nonconvex equality constrained optimization

Mathematical Programming

Volumn 122, Issue 2, 2010, Pages 273-299

  Byrd, Richard H ^a   Curtis, Frank E ^b   Nocedal, Jorge ^b  

^a University of Colorado at Boulder   (United States)

^b Northwestern University   (United States)

Author keywords

Constrained optimization; Inexact linear system solvers; Krylov subspace methods; Large scale optimization; Nonconvex programming

Indexed keywords

CONVEX PROBLEMS; EQUALITY-CONSTRAINED OPTIMIZATION; EXACT PENALTIES; GLOBAL BEHAVIORS; INEXACT LINEAR SYSTEM SOLVERS; INEXACT NEWTON METHOD; ITERATION MATRICES; KRYLOV SUBSPACE METHODS; LARGE-SCALE OPTIMIZATION; LINE SEARCH ALGORITHM; MATRIX; NEGATIVE CURVATURE; NONCONVEX; NONCONVEX PROBLEM; NONCONVEX PROGRAMMING; NUMERICAL RESULTS; PRIMAL-DUAL; SECOND DERIVATIVES; SECOND ORDERS; SEQUENTIAL QUADRATIC PROGRAMMING; TEST PROBLEM;

LEARNING ALGORITHMS; LINEAR SYSTEMS; NEWTON-RAPHSON METHOD; QUADRATIC PROGRAMMING;

CONSTRAINED OPTIMIZATION;

EID: 69949096738     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-008-0248-3     Document Type: Article

References (22)

1. I. Bongartz A.R. Conn N.I.M. Gould Ph.L. Toint 1995 CUTE: constrained and unconstrained testing environment ACM Trans. Math. Softw. 21 1 123 160
2. R.H. Byrd F.E. Curtis J. Nocedal 2008 An inexact SQP method for equality constrained optimization SIAM J. Optim. 19 1 351 369
3. Conn A.R., Gould N.I.M., Toint Ph.: Trust-Region Methods. MPS-SIAM Series on Optimization. SIAM Publications, Philadelphia (2000)
4. Curtis, F.E., Haber, E.: Numerical experience with an inexact SQP method for PDE-constrained optimization. (In preparation)
5. J.E. Dennis L.N. Vicente 1997 On the convergence theory of trust-region based algorithms for equality-constrained optimization SIAM J. Optim. 7 4 927 950
6. J. Di-Pillo S. Lucidi L. Palagi 2005 Convergence to second-order stationary points of a primal-dual algorithm model for nonlinear programming Math. Oper. Res. 30 4 879 915
7. E.D. Dolan J.J. Moré 2002 Benchmarking optimization software with performance profiles Math. Program. Ser. A 91 201 213
8. M. El-Alem 1996 Convergence to a 2nd order point of a trust-region algorithm with nonmonotonic penalty parameter for constrained optimization J. Optim. Theory Appl. 91 1 61 79 (Pubitemid 126323626)
9. F. Facchinei S. Lucidi 1998 Convergence to second order stationary points in inequality constrained optimization Math. Oper. Res. 23 746 766
10. Freund, R.W., Nachtigal, N.M.: A new Krylov-subspace method for symmetric indefinite linear systems. In: Ames, W.F. (ed.) Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, pp. 1253-1256. IMACS (1994)
11. N.I.M. Gould D. Orban Ph.L. Toint 2003 CUTEr and sifdec: a constrained and unconstrained testing environment, revisited ACM Trans. Math. Softw. 29 4 373 394
12. N.I.M. Gould Ph.L. Toint 1999 A note on the second-order convergence of optimization algorithms using barrier functions Math. Program. 85 2 433 438
13. Heinkenschloss, M., Ridzal, D.: An inexact trust-region SQP method with applications to PDE-constrained optimization. In: Steinbach, O., Of, G. (eds.) Numerical Mathematics and Advance Applications: Proceedings of Enumath 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007, Springer, Heidelberg (2008, submitted). doi: 10.1007/978-3-540-69777-0-73
14. M. Heinkenschloss L.N. Vicente 2001 Analysis of inexact trust-region SQP algorithms SIAM J. Optim. 12 283 302
15. Kelley, C.T.: Iterative methods for linear and nonlinear equations: Matlab codes (1994). http://www4.ncsu.edu/~ctk/matlab-roots.html
16. J.M. Moguerza F.J. Prieto 2003 An augmented Lagrangian interior point method using directions of negative curvature Math. Program. 95 3 573 616
17. C.C. Paige M.A. Saunders 1975 Solution of sparse indefinite systems of linear equations SIAM J. Numer. Anal. 12 4 617 629
18. Paige, C.C., Saunders, M.A.: MINRES: sparse symmetric equations (2003). http://www.stanford.edu/group/SOL/software/minres.html
19. Ridzal, D.: Trust region SQP methods with inexact linear system solves for large-scale optimization. Ph.D. thesis, Rice University (2006)
20. Y. Saad M.H. Schultz 1986 GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems SIAM J. Sci. Stat. Comput. 7 856 869
21. S. Ulbrich 2008
22. R.J. Vanderbei D.F. Shanno 1999 An interior point algorithm for nonconvex nonlinear programming Comput. Optim. Appl. 13 231 252