Convergence to a second-order point of a trust-region algorithm with a nonmonotonic penalty parameter for constrained optimization

Journal of Optimization Theory and Applications

Volumn 91, Issue 1, 1996, Pages 61-79

  El Alem, M M ^a  

^a Alexandria University Faculty Of Science   (Egypt)

Author keywords

Constrained optimization; Convergence; Equality constrained problems; First order point; Necessary conditions; Nonmonotonic penalty parameters; Penalty parameters; Second order point; Trust region methods

Indexed keywords

ITERATIVE METHODS; PARAMETER ESTIMATION;

CONDITION; CONVERGENCE; EQUALITY-CONSTRAINED PROBLEM; FIRST ORDER; FIRST-ORDER POINT; NECESSARY CONDITION; NONMONOTONIC; NONMONOTONIC PENALTY PARAMETER; PENALTY PARAMETERS; SECOND ORDERS; SECOND-ORDER POINT; TRUST-REGION METHODS;

CONSTRAINED OPTIMIZATION;

EID: 0039056352     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02192282     Document Type: Article

References (31)

1. EL-ALEM, M. M., A Robust Trust-Region Algorithm with a Nonmonotonic Penalty Parameter Scheme for Constrained Optimization, SIAM Journal on Optimization, Vol. 5, pp. 348-378, 1995.
2. FIACCO, A., and MCCORMICK, G., Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley, New York, New York, 1968.
3. DENNIS, J., EL-ALEM, M. M., and MACIEL, M., A Global Convergence Theory for General Trust-Region-Based Algorithms for Equality Constrained Optimization, Technical Report 92-28, Department of Computational and Applied Mathematics, Rice University, Houston, Texas, 1992.
4. WILSON, R. B., A Simplified Algorithm for Concave Programming, PhD Thesis, Harvard University, Cambridge, Massachusetts, 1963.
5. TAPIA, R. A., Quasi-Newton Methods for Equality Constrained Optimization: Equivalence of Existing Methods and a New Implementation, Nonlinear Programming 3, Edited by O. L. Mangasarian, R. Meyer, and S. M. Robinson, Academic Press, New York, New York, pp. 125-146, 1978.
6. MIELE, A., HUANG, H. Y., and HEIDEMAN, J. C., Sequential Gradient-Restoration Algorithm for the Minimization of Constrained Functions: Ordinary and Conjugate Gradient Versions, Journal of Optimization Theory and Applications, Vol. 4, pp. 213-243, 1969.
7. VARDI, A., A Trust-Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation, SIAM Journal on Numerical Analysis, Vol. 22, pp. 575-591, 1985.
8. BYRD, R., SCHNABEL, B., and SHULTZ, G., A Trust-Region Algorithm for Nonlinearly Constrained Optimization, SIAM Journal on Numerical Analysis, Vol. 24, pp. 1152-1170, 1987.
9. CELIS, M., DENNIS, J., and TAPIA, R., A Trust-Region Strategy for Nonlinear Equality Constrained Optimization, Numerical Optimization, Edited by P. Boggs, R. Byrd, and R. Schnabel, SIAM, Philadelphia, Pennsylvania, pp. 71-82, 1985.
10. EL-ALEM, M. M., A Global Convergence Theory for a Class of Trust-Region Algorithms for Constrained Optimization, PhD Thesis, Department of Computational and Applied Mathematics, Rice University, Houston, Texas, 1988.
11. EL-ALEM, M. M., A Global Convergence Theory for the Celis-Dennis-Tapia Trust-Region Algorithm for Constrained Optimization, SIAM Journal on Numerical Analysis, Vol. 24, pp. 266-290, 1991.
12. POWELL, M. J. D., and YUAN, Y., A Trust-Region Algorithm for Equality Constrained Optimization, Mathematical Programming, Vol. 49, pp. 189-211, 1991.
13. EL-ALEM, M. M., and TAPIA, R. A., Numerical Experience with a Polyhedral Norm CDT Trust-Region Algorithm, Journal of Optimization Theory and Applications, Vol. 85, pp. 575-592, 1995.
14. YUAN, Y., A Dual Algorithm for Minimizing a Quadratic Function with Two Quadratic Constraints, Technical Report DAMTP-NA3, University of Cambridge, Cambridge, England, 1988.
15. YUAN, Y., On a Subproblem of Trust-Region Algorithms for Constrained Optimization, Mathematical Programming, Vol. 47, pp. 53-63, 1990.
16. ZHANG, Y., Computing a Celis-Dennis-Tapia Trust-Region Step for Equality Constrained Optimization, Mathematical Programming, Vol. 55, pp. 109-124, 1992.
17. WILLIAMSON, K. A., A Robust Trust-Region Algorithm for Nonlinear Programming, PhD Thesis, Department of Mathematical Sciences, Rice University, Houston, Texas, 1990.
18. ALEXANDROV, N., Multi-Level Algorithms for Nonlinear Equations and Equality Constrained Optimization, PhD Thesis, Department of Computational and Applied Mathematics, Rice University, Houston, Texas, 1993.
19. ALEXANDROV, N., and DENNIS, J. E., Multi-Level Algorithms for Nonlinear Optimization, Technical Report 94-24, Department of Computational and Applied Mathematics, Rice University, Houston, Texas, 1994.
20. BYRD, R., and OMOJOKUN, E., Robust Trust-Region Methods for Nonlinearly Constrained Optimization, Paper Presented at the SIAM Conference on Optimization, Houston, Texas, 1987.
21. DENNIS, J., and VICENTE, L., On the Convergence Theory of Trust-Region-Based Algorithms for Equality-Constrained Optimization, Technical Report 94-36, Department of Computational and Applied Mathematics, Rice University, Houston, Texas, 1994.
22. EL-ALEM, M. M., Global Convergence without the Assumption of Linear Independence for a Trust-Region Algorithm for Constrained Optimization, Journal of Optimization Theory and Applications, Vol. 87, pp. 563-577, 1995.
23. MACIEL, M. C., A Global Convergence Theory for a General Class of Trust-Region Algorithms for Equality Constrained Optimization, PhD Thesis, Department of Computational and Applied Mathematics, Rice University, Houston, Texas, 1992.
24. OMOJOKUN, E., Trust-Region Strategies for Optimization with Nonlinear Equality and Inequality Constraints, PhD Thesis, Department of Computer Science, University of Colorado, Boulder, Colorado, 1989.
25. ZHANG, J., and ZHU, D., Projected Quasi-Newton Algorithm with Trust Region for Constrained Optimization, Journal of Optimization Theory and Applications, Vol. 67, pp. 369-393, 1990.
26. FLETCHER, R., Practical Methods of Optimization, Vol. 1: Unconstrained Optimization, John Wiley and Sons, New York, New York, 1980.
27. MORÉ, J. J., Recent Developments in Algorithms and Software for Trust-Region Methods, Mathematical Programming: The State of The Art, Edited by A. Bachem, M. Grotschel, and B. Korte, Springer Verlag, New York, New York, pp. 258-287, 1983.
28. COLEMAN, T., and SORENSEN, D., A Note on the Computation of an Orthonormal Basis for the Null Space of a Matrix, Mathematical Programming, Vol. 29, pp. 234-242, 1984.
29. MORÉ, J. J., and SORENSEN, D., Computing a Trust-Region Step, SIAM Journal on Statistical and Scientific Computing, Vol 4, pp. 553-572, 1983.
30. SHULTZ, G., SCHNABEL, R., and BYRD, R., A Family of Trust-Region-Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties, SIAM Journal on Numerical Analysis, Vol. 22, pp. 47-67, 1985.
31. SORENSEN, D., Newton's Method with a Model Trust-Region Modification, SIAM Journal on Numerical Analysis, Vol. 19, pp. 409-426, 1982.