On the formulation and theory of the newton interior-point method for nonlinear programming

Journal of Optimization Theory and Applications

Volumn 89, Issue 3, 1996, Pages 507-541

  El Bakry, A S ^a,b   Tapia, R A ^b   Tsuchiya, T ^c   Zhang, Y ^b,d  

^a Alexandria University Faculty Of Science   (Egypt)

^b RICE UNIVERSITY   (United States)

^c INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

^d UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

Global convergence; Interior point methods; Nonlinear programming; Primal dual methods; Superlinear and quadratic convergence

Indexed keywords

LINEAR PROGRAMMING; NEWTON-RAPHSON METHOD;

DAMPED NEWTON'S METHODS; GLOBAL CONVER-GENCE; INTERIOR-POINT METHOD; KARUSH KUHN TUCKER CONDITION; LINEAR-PROGRAMMING; LOGARITHMIC BARRIER FUNCTION; NEWTON INTERIOR-POINT METHODS; PRIMAL-DUAL INTERIOR POINT METHODS; PRIMAL-DUAL METHODS; SUPERLINEAR AND QUADRATIC CONVERGENCE;

NONLINEAR PROGRAMMING;

EID: 0030541525     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02275347     Document Type: Article

References (25)

1. LUSTIG, J., MARSTEN, R. E., and SHANNO, D. F., On Implementing Mehrotra's Predictor-Corrector Interior-Point Method for Linear Programming, SIAM Journal on Optimization, Vol. 2, pp. 435-449, 1992.
2. WRIGHT, M. H., Interior Methods for Constrained Optimization, Numerical Analysis Manuscript 91-10, ATT Bell Laboratories, Murray Hill, New Jersey, 1991.
3. NASH, S. G., and SOFER, A., A Barrier Method for Large-Scale Constrained Optimization, Technical Report 91-10, Department of Operations Research and Applied Statistics, George Mason University, Fairfax, Virginia, 1991.
4. WRIGHT, S. J., A Superlinear Infeasible-Interior-Point Algorithm for Monotone Nonlinear Complementarity Problems, Technical Report MCS-P344-1292, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, 1992.
5. MONTEIRO, R. C., PANG, J., and WANG, T., A Positive Algorithm for the Nonlinear Complementarity Problem, Technical Report, Department of Systems and Industrial Engineering, University of Arizona, Tucson, Arizona, 1992.
6. WRIGHT, S. J., An Interior-Point Algorithm for Linearly Constrained Optimization, SIAM Journal on Optimization, Vol. 2, pp. 450-473, 1992.
7. LASDON, L., Yu, G., and PLUMMER, J., An Interior-Point Algorithm for Solving General Nonlinear Programming Problems, Paper Presented at the SIAM Conference on Optimization, Chicago, Illinois, 1992.
8. YAMASHITA, H., A Globally Convergent Primal-Dual Interior Point Method for Constrained Optimization, Technical Report, Mathematical Systems Institute, Tokyo, Japan, 1992.
9. MCCORMICK, G. P., The Superlinear Convergence of a Nonlinear Primal-Dual Algorithm, Technical Report T-550/91, School of Engineering and Applied Science, George Washington University, Washington, DC, 1991.
10. ANSTREICHER, K. M., and VIAL, J., On the Convergence of an Infeasible Primal-Dual Interior-Point Method for Convex Programming, Optimizations Methods and Software, (to appear).
11. KOJIMA, M., MEGIDDO, N., and NOMA, N., Homotopy Continuation Methods for Nonlinear Complementarity Problems, Mathematics of Operations Research, Vol. 16, pp. 754-774, 1991.
12. MONTEIRO, R. C., and WRIGHT, S. J., A Globally and Superlinearly Convergent Potential Reduction Interior-Point Method for Convex Programming, Unpublished Manuscript, 1992.
13. KOJIMA, M., MIZUNO, S., and YOSHISE, A., A Primal-Dual Interior-Point Method for Linear Programming, Progress in Mathematical Programming, Interior-Point and Related Methods, Edited by N. Megiddo, Springer Verlag, New York, New York, 1989.
14. FIACCO, A. V., and MCCORMICK, G. P., Nonlinear Programming: Sequential Unconstrained Minimization Technique, John Wiley and Sons, New York, New York, 1968.
15. MEGIDDO, N., Pathways to the Optimal Set in Linear Programming, Progress in Mathematical Programming, Interior-Point and Related Methods, Edited by N. Megiddo, Springer Verlag, New York, New York, 1989.
16. HESTENES, M. R., Multiplier and Gradient Methods, Journal of Optimization Theory and Applications, Vol. 4, pp. 303-329, 1969.
17. TAPIA, R. A., On the Role of Slack Variables in Quasi-Newton Methods for Constrained Optimization, Numerical Optimization of Dynamic Systems; Edited by L. C. W. Dixon and G. P. Szegö, North Holland, Amsterdam, Holland, 1980.
18. EL-BAKRY, A. S., TAPIA, R. A., and ZHANG, Y., A Study of Indicators for Identifying Zero Variables in Interior-Point Methods, SIAM Review, Vol. 36, pp. 45-72, 1994.
19. ZHANG, Y., TAPIA, R. A., and DENNIS, J. E., JR., On the Superlinear and Quadratic Convergence of Primal-Dual Interior-Point Linear Programming Algorithms, SIAM Journal on Optimization, Vol. 2, pp. 304-324, 1992.
20. ZHANG, Y., and TAPIA, R. A., Superlinear and Quadratic Convergence of Primal-Dual Interior-Point Algorithms for Linear Programming Revisited, Journal of Optimization Theory and Applications, Vol. 73, pp. 229-242, 1992.
21. DENNIS, J. E., JR., and SCHNABEL, R. B., Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1983.
22. ORTEGA, J. M., and RHEINBOLDT, W. C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, New York, 1970.
23. BYRD, R. H., and NOCEDAL, J., A Tool for the Analysis of Quasi-Newton Methods with Application to Unconstrained Minimization, SIAM Journal on Numerical Analysis, Vol. 26, pp. 727-739, 1989.
24. HOCK, W., and SCHITTKOWSKI, K., Test Examples for Nonlinear Programming Codes, Springer Verlag, New York, New York, 1981.
25. SCHITTKOWSKI, K., More Test Examples for Nonlinear Programming Codes, Springer Verlag, New York, New York, 1987.