Summary
The global convergence properties of a penalty-barrier method for solving equality and/or inequality constrained nonlinear optimization problems are considered. The presented algorithm is a composite of augmented Lagrangian, modified log-barrier, and classical log-barrier methods. Under common conditions, global convergence of a sequence of iterates to a first-order stationary point for the constrained problem is established. The iterates are approximate minima of a sequence of unconstrained penalty-barrier functions. Extensive computational tests suggest that the presented penalty-barrier algorithm is a robust and efficient method for solving general nonlinear optimization problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Ben-Tal, I. Yuzefovich, and M. Zibulevsky, Penalty/barrier multiplier methods for minimax and constrained smooth convex problems, Research Report 9/92, Optimization Laboratory, Faculty of Industrial Engineering and Management, Technion, Haifa, Israel, 1992.
D. P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods, Academic Press, London, New York, 1982.
M. G. Breitfeld and D. F. Shanno, Computational experience with penalty-barrier methods for nonlinear programming, RUTCOR Research Report RRR 17–93 (revised March 1994), Rutgers Center for Operations Research, Rutgers University, New Brunswick, New Jersey, 1993. Submitted to Annals of Operations Research.
M. G. Breitfeld and D. F. Shanno A globally convergent penalty-barrier algorithm for nonlinear programming and its computational performance, RUTCOR Research Report RRR 12–94, Rutgers Center for Operations Research, Rutgers University, New Brunswick, New Jersey, 1994. Submitted to Mathematical Programming.
M. G. Breitfeld and D. F. Shanno, Preliminary computational experience with modified log-barrier functions for large-scale nonlinear programming, in Large Scale Optimization: State of the Art, W. W. Hager, D. W. Hearn, and P. M. Pardalos, eds., Kluwer Academic Publishers B.V., 1994, pp. 45–67.
A. V. Fiacco and G. P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley & Sons, New York, 1968. Reprint: Volume 4 of SIAM Classics in Applied Mathematics, SIAM Publications, Philadelphia, Pennsylvania, 1990.
K. R. Frisch, The logarithmic potential method for convex programming, unpublished manuscript, Institute of Economics, University of Oslo, Oslo, Norway, May 1955.
S. G. Nash, R. Polyak, and A. Sofer, A numerical comparison of barrier and modified- barrier methods for large-scale bound-constrained optimization, in Large Scale Optimization: State of the Art, W. W. Hager, D. W. Hearn, and P. M. Pardalos, eds., Kluwer Academic Publishers B.V., 1994, pp. 319–338.
R. Polyak, Modified barrier functions (theory and methods), Mathematical Programming, 54 (1992), pp. 177–222.
M. H. Wright, Interior methods for constrained optimization, in Acta Numerica, A. Iserles, ed., Cambridge University Press, New York, 1992, pp. 341–407.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Breitfeld, M.G., Shanno, D.F. (1995). A Globally Convergent Penalty-Barrier Algorithm for Nonlinear Programming. In: Derigs, U., Bachem, A., Drexl, A. (eds) Operations Research Proceedings 1994. Operations Research Proceedings, vol 1994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79459-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-79459-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58793-4
Online ISBN: 978-3-642-79459-9
eBook Packages: Springer Book Archive