On the convergence of the Newton/log-barrier method

Mathematical Programming, Series B

Volumn 90, Issue 1, 2001, Pages 71-100

  Wright, Stephen J ^a  

^a ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012742914     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00011421     Document Type: Article

References (29)

1. Benchakroun, A., Dussault, J.-P., Mansouri, A. (1995): A two parameter mixed interior-exterior penalty algorithm. ZOR - Math. Methods Oper. Res. 41, 25-55
2. Broyden, C., Attia, N. (1983): A smooth sequential penalty function method for solving nonlinear programming problems. In: Thoft-Christenses, P., ed., System Modeling and Optimization, pp. 237-245. Springer, Berlin
3. Byrd, R.H., Hribar, M.E., Nocedal, J. (1997): An interior point algorithm for large scale nonlinear programming. OTC Technical Report 97/05, Optimization Technology Center
4. Conn, A.R., Gould, N.I.M., Orban, D., Toint, Ph. L. (1999): A primal-dual trust-region algorithm for minimizing a non-convex function subject to general inequality and linear equality constraints. Technical Report RAL-TR-1999-054, Computational Sciences and Engineering Department, Atlas Center, Rutherford Appleton Laboratory
5. Conn, A.R., Gould, N.I.M., Toint, Ph.L. (1994): A note on using alternative second-order models for the subproblems arising in barrier function methods for minimization. Numer. Math. 68, 17-33
6. den Hertog, D., Roos, C., Terlaky, T. (1992): A large-step analytic center method for a class of smooth convex programming problems. SIAM J. Optim. 2, 55-70
7. den Hertog, D., Roos, C., Terlaky, T. (1992): On the classical logarithmic barrier function method for a class of smooth convex programming problems. J. Optim. Theory Appl. 73, 1-25
8. Dennis, J.E., Schnabel, R.B. (1983): Numerical Methods for Unconstrained Optimization. Prentice-Hall, Englewood Cliffs, NJ
9. Dussault, J.-P. (1995): Numerical stability and efficiency of penalty algorithms. SIAM J. Numer. Anal. 32, 296-317
10. Fiacco, A.V., McCormick, G.P. (1968): Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York. Reprinted by SIAM Publications, 1990
11. Fletcher, R. (1987): Practical Methods of Optimization. John Wiley and Sons, New York, second edition
12. Forsgren, A., Gill, P.E. (1998): Primal-dual interior-point methods for nonconvex nonlinear programming. SIAM J. Optim. 8, 1132-1152
13. Gay, D.M., Overton, M.L., Wright, M.H. (1997): A primal-dual interior method for nonconvex nonlinear programming. Technical Report 97-4-08, Computing Sciences Research, Bell Laboratories, Murray Hill, NJ, July 1997
14. Gould, N.I.M. (1986): On the accurate determination of search directions for simple differentiable penalty functions. IMA J. Numer. Anal. 6, 357-372
15. Gould, N.I.M. (1989): On the convergence of a sequential penalty function method for constrained minimization. SIAM J. Numer. Anal. 26, 107-128
16. Jarre, F. (1992): Interior-point methods for convex programming. Appl. Math. Optim. 26, 287-311
17. Jittorntrum, K., Osborne, M.R. (1978): Trajectory analysis and extrapolation in barrier function methods. J. Aust. Math. Soc. Ser. B 20, 352-369
18. Lootsma, F.A. (1969): Hessian matrices of penalty functions for solving constrained optimization problems. In: Philips Research Reports, vol. 24, pp. 322-331. Philips, Eindhoven, The Netherlands
19. Murray, W. (1971): Analytical expressions for the eigenvalues and eigenvectors of the Hessian matrices of barrier and penalty functions. J. Optim. Theory Appl. 7, 189-196
20. Murray, W., Wright, M.H. (1994): Line search procedures for the logarithmic barrier function. SIAM J. Optim. 4, 229-246
21. Nash, S.G., Sofer, A. (1993): A barrier method for large-scale constrained optimization. ORSA J. Comput. 5, 40-53
22. Nash, S.G., Sofer, A. (1998): Why extrapolation helps barrier methods. Technical report, Operations Research and Engineering Department, George Mason University, September 1998
23. Nesterov, Yu.E., Nemirovskii, A.S. (1994): Interior Point Polynomial Methods in Convex Programming. SIAM Publications, Philadelphia
24. Wright, M.H. (1992): Interior methods for constrained optimization. In: Acta Numerica 1992, pp. 341-407. Cambridge University Press, Cambridge
25. Wright, M.H. (1994): Some properties of the Hessian of the logarithmic barrier function. Math. Program. 67, 265-295
26. Wright, M.H. (1995): Why a pure primal Newton barrier step may be infeasible. SIAM J. Optim. 5, 1-12
27. Wright, M.H. (1998): Ill-conditioning and computational error in interior methods for nonlinear programming. SIAM J. Optim. 9, 84-111
28. Wright, S.J. (1998): Effects of finite-precision arithmetic on interior-point methods for nonlinear programming. Preprint ANL/MCS-P705-0198, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill., January 1998. To appear in SIAM J. Optim.
29. Wright, S.J., Jarre, F. (1998): The role of linear objective functions in barrier methods. Math. Program. 84, 357-373