Global convergence analysis of line search interior-point methods for nonlinear programming without regularity assumptions

Journal of Optimization Theory and Applications

Volumn 125, Issue 3, 2005, Pages 609-628

  Liu, X W ^a,b   Sun, J ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b HEBEI UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Convergence; Interior point methods; Nonlinear programming

Indexed keywords

CONVERGENCE; CONVERGENCE ANALYSIS; GLOBAL CONVER-GENCE; INTERIOR-POINT METHOD; LIMIT POINTS; LINE SEARCHES; MERIT FUNCTION; PRIMAL-DUAL; REGULARITY ASSUMPTION; SEARCH STRATEGIES;

NONLINEAR PROGRAMMING;

EID: 21444446016     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-005-2092-4     Document Type: Article

References (17)

1. WÄCHTER, A., and BIEGLER, L. T., Failure of Global Convergence for a Class of Interior-Point Methods for Nonlinear Programming, Mathematical Programming, Vol. 88, pp. 565-574, 2000.
2. FIACCO, A. V., and MCCORMICK, G. P., Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley and Sons, New York, NY, 1968; republished by SIAM, Philadelphia, Pennsylvania, 1990.
3. BYRD, R. H., GILBERT, J. C., and NOCEDAL, J., A Trust-Region Method Based on Interior-Point Techniques for Nonlinear Programming, Mathematical Programming, Vol. 89, pp. 149-185, 2000.
4. TSENG, P., Convergent Infeasible Interior-Point Trust-Region Methods for Constrained Minimization, SIAM Journal on Optimization, Vol. 13, pp. 432-469, 2002.
5. LIU, X. W., and SUN, J., A Robust Primal-Dual Interior-Point Algorithm for Nonlinear Programs, SIAM Journal on Optimization, Vol.14, pp. 1163-1186, 2004.
6. BYRD, R. H., HRIBAR, M. E., and NOCEDAL, J., An Interior-Point Algorithm for Large-Scale Nonlinear Programming, SIAM Journal on Optimization, Vol. 9, pp. 877-900, 1999.
7. BYRD, R. H., MARAZZI, M., and NOCEDAL, J., On the Convergence of Newton Iterations to Nonstationary Points, Report OTC 2001/01, Optimization Technology Center, Northwestern University, Evanston, Illinois.
8. CONN, A. R., GOULD, N., and TOINT, P. L., A Primal-Dual Algorithm for Minimizing a Nonconvex Function Subject to Bound and Linear Equality Constraints, Nonlinear Optimization and Applications 2, Edited by G. Di PILLO and F. GIANNESSI, Kluwer Academic Publishers, Dordrecht, Holland, 1999.
9. EL-BARKY, A. S., TAPIA, R. A., TSUCHIYA, T., and ZHANG, Y., On the Formulation and Theory of the Newton Interior-Point Method for Nonlinear Programming, Journal of Optimization Theory and Applications, Vol. 89, pp. 507-541, 1996.
10. FORSGREN, A., and GILL, P. E., Primal-Dual Interior Methods for Nonconvex Nonlinear Programming, SIAM Journal on Optimization, Vol. 8, pp. 1132-1152, 1998.
11. GAY, D. M., OVERTON, M. L., and WRIGHT, M. H., A Primal-Dual Interior Method for Nonconvex Nonlinear Programming, Advances in Nonlinear Programming: Proceedings of the 1996 International Conference on Nonlinear Programming, Edited by Y. Yuan, Kluwer Academic Publishers, Dordrecht, Holland, 1998.
12. LASDON, L. S., PLUMMER, J., and YU, G., Primal-Dual and Primal Interior-Point Algorithms for General Nonlinear Programs, ORSA Journal on Computing, Vol. 7, pp. 321-332, 1995.
13. SHANNO, D. F., and VANDERBEI, R. J., Interior-Point Methods for Nonconvex Nonlinear Programming: Orderings and Higher-Order Methods, Mathematical Programming, Vol. 87, pp. 303-316, 2000.
14. VANDERBEI, R. J., and SHANNO, D. F., An Interior-Point Algorithm for Nonconvex Nonlinear Programming, Computational Optimization and Applications, Vol. 13, pp. 231-252, 1999.
15. YAMASHITA, H., A Global Convergent Primal-Dual Interior-Point Method for Constrained Optimization, Optimization Methods and Software, Vol. 10, pp. 448-469, 1998.
16. LIU, X. W., and YUAN, Y., A Robust Algorithm for Optimization with General Equality and Inequality Constraints, SIAM Journal on Statistical and Scientific Computing, Vol. 22, pp. 517-534, 2000.
17. LIU, X. W., and SUN, J., Global Convergence Analysis of Line Search Interior-Point Methods for Nonlinear Programming without Regularity Assumptions: A Complete Version, School of Business, National University of Singapore, 2004.