Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization

Optimization Methods and Software

Volumn 11, Issue 1, 1999, Pages 275-302

  Altman, Anna ^a   Gondzio, Jacek ^b  

^a SYSTEMS RESEARCH INSTITUTE   (Poland)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; QUADRATIC PROGRAMMING;

INTERIOR POINT METHODS; SYMMETRIC QUASIDEFINITE SYSTEMS;

LINEAR PROGRAMMING;

EID: 0033296703     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/10556789908805754     Document Type: Article

References (30)

1. Altman, A. (1995). QHOPDM -A higher order primal-dual method for large scale separable convex quadratic programming, European Journal of Operational Research, 87, 200-202.
2. Altman, A. (1996). Higher order primal-dual interior point method for separable convex quadratic optimization, Control and Cybernetics, 25(4), 761-772.
3. Altman, A. Amann, M. Klaassen, G. Ruszczyński, and Schöpp, W. (1996). Cost-effective sulphur emission reduction under uncertainty, European Journal of Operational Research, 90, 395-412.
4. Andersen, E. Gondzio, J. Mészáros, C. and Xu, X. (1996). Implementation of interior point methods for large scale linear programming, In T. Terlaky, editor, Kluwer Academic Publishers, Interior Point Methods in Mathematical Programming, pp. 189-252.
5. Arioli, M. Demmel, J. W. and Duff, I. S. (1989). Solving sparse linear systems with sparse backward error, SIAM Journal on Matrix Analysis and Applications, 10(2), 165-190.
6. Arioli, M. Duff, I. S. and de Rijk, P. P. M. (1989). On the augmented system approach to sparse least-squares problems, Numerische Mathematik, 55, 667-684.
7. Bunch J. R. and Parlett, B. N. (1971). Direct methods for solving symemtric indefinite systems of linear equations, SIAM Journal on Numerical Analysis, 8, 639-655.
8. Carpenter, T. J. Lustig, I. J. Mulvey, J. M. and Shanno, D. F. (1993). Higher order predictor-corrector interior point methods with application to quadratic programming, SIAM Journal on Optimization, 3, 696-725.
9. Fiacco, A. V. and McCormick, G. P. (1968). Nonlinear Programming, Sequential Unconstrained Minimization Techniques, John Wiley and Sons, New York.
10. Fourer, R. and Mehrotra, S. (1993). Solving symmetric indefinite systems in an interior-point method for linear programming, Mathematical Programming, 62, 15-39.
11. Gay, D. M. (1985). Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter, 13, 10-12.
12. Gondzio, J. (1993). Implementing Cholesky factorization for interior point methods of linear programming, Optimization, 27, 121-140.
13. Gondzio, J. (1995). HOPDM (version 2.12) - a fast LP solver based on a primal-dual interior point method, European Journal of Operational Research, 85, 221-225.
14. Gondzio, J. (1996). Multiple centrality corrections in a primal-dual method for linear programming, Computational Optimization and Applications, 6, 137-156.
15. Kojima, M. Mizuno, S. and Yoshise, A. (1989). A primal-dual interior point algorithm for linear proramming. In N. Megiddo, editor, Progress in Mathematical Programming, Interior-Point Algorithms and Related Methods, pp 29-47. Springer Verlag, Berlin, Germany.
16. Lustig, I. J. Marsten, R. E. and Shanno, D. F. (1992). On implementing Mehrotra's predictor-corrector interior point method for linear programming, SIAM Journal on Optimization, 2, 435-449.
17. Lustig, I. J. Marsten, R. E. and Shanno, D. F. (1994). Interior point methods for linear programming, computational state of the art, ORSA Journal on Computing, 6, 1-14.
18. Maros, I. and Mészáros, C. (1997). A repository of convex quadratic programming problems, Technical Report DOC 97/6, Department of Computing, Imperial College, London, U.K., July.
19. Megiddo, N. (1989). Pathways to the optimal set in linear programming. In N. Megiddo, editor, Progress in Mathematical Programming, Interior-Point Algorithms and Related Methods, Springer Verlag, Berlin, Germany.
20. Mehrotra, S. (1992). On the implementation of a primal-dual interior point method, SIAM Journal on Optimization, 2, 575-601.
21. Mittelmann, H. (1998). Decision tree for optimization software, January.
22. Rockafellar, R. T. (1976). Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Mathematics of Operations Research, 1, 97-116.
23. Rockafellar, R. T. (1976). Monotone operators and the proximal point algorithm in convex programming, SIAM Journal on Control and Optimization, 14, 887-898.
24. Saunders, M. (1996). Cholesky-based methods for sparse least squares, the benefits of regularization, In L. Adams and L. Nazareth, editors, Linear and Nonlinear Conjugate Gradient-Related Methods, pp 92-100. SIAM, Philadelphia, USA.
25. Saunders, M. and Tomlin, J. A. (1996). Solving regularized linear programs using barrier methods and KKT systems, Technical Report SOL 96-4, Systems Optimization Laboratory, Dept. of Operatoions Research, Stanford University, Stanford, CA 94305, USA, December.
26. Setiono, R. (1992). Interior proximal point algorithm for linear programs. Journal of Optimization Theory and Application, 74, 425-444.
27. Vanderbei, R. J. (1994). LOQO: An interior point code for quadratic programming, Technical Report SOR-94-15, Statistics and Operations Research, Princeton University.
28. Vanderbei, R. J. (1995). Symmetric quasidefinite matrices, SIAM Journal on Optimization, 5, 100-113.
29. Vanderbei R. J. and Carpenter, T. J. (1993). Symmetric indefinite systems for interior point methods, Mathematical Programming, 58, 1-32.
30. Wright, S. (1997). Primal-Dual Interior-Point Methods. SIAM, Philadelphia.