Parallel interior-point method for linear and quadratic programs with special structure

Journal of Optimization Theory and Applications

Volumn 110, Issue 2, 2001, Pages 289-313

  Durazzi, C ^a   Ruggiero, V ^a   Zanghirati, G ^a  

^a UNIVERSITY OF FERRARA   (Italy)

Author keywords

Inexact Newton methods; Interior point methods; Parallel computing; Planning under uncertainty; Preconditioned conjugate gradient method

Indexed keywords

COMPUTATION THEORY; CONJUGATE GRADIENT METHOD; LINEAR PROGRAMMING; NEWTON-RAPHSON METHOD; QUADRATIC PROGRAMMING;

INEXACT NEWTON METHOD; INTERIOR-POINT METHOD; ITERATIVE SOLVERS; LINEAR PROGRAMMING PROBLEM; LINEAR PROGRAMS; PARALLEL COM- PUTING; PLANNING UNDER UNCERTAINTY; PRECONDITIONED CONJUGATE GRADIENT METHOD; QUADRATIC PROGRAMS; SPECIAL STRUCTURE;

STOCHASTIC SYSTEMS;

EID: 0035536764     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017523228692     Document Type: Article

References (26)

1. 1. POTRA, F., ROOS, C., and TERLAKY, T., Editors, Special Issue on Interior-Point Methods, Optimization Method and Software, Vols. 11-12, pp. 451-484, 1999.
2. 2. CENSOR, Y., and ZENIOS, S. A., Parallel Optimization: Theory, Algorithms, and Applications, Oxford University Press, Oxford, England, 1997.
3. 3. BELLAVIA, S., Inexact Interior-Point Method, Journal of Optimization Theory and Applications, Vol. 96, pp. 109-121, 1998.
4. 4. DURAZZI, C., On the Newton Interior-Point Method for Nonlinear Programming Problems, Journal of Optimization Theory and Applications, Vol. 104, pp. 73-90, 2000.
5. 5. DEMBO, R. S., EISENSTAT, S. C., and STEIHAUG, T., Inexact Newton Methods, SIAM Journal on Numerical Analysis, Vol. 19, pp. 400-408, 1982.
6. 6. EISENSTAT, S. C., and WALKER, H. F., Globally Convergent Inexact Newton Methods, SIAM Journal on Optimization, Vol. 4, pp. 393-422, 1994.
7. 7. EL-BAKRY, A. S., TAPIA, R. A., TSUCHIYA, T., and ZHANG, Y., On the Formulation and Theory of Newton Interior-Point Method for Nonlinear Programming, Journal of Optimization Theory and Applications, Vol. 89, pp. 507-541, 1996.
8. 8. LUSTIG, I. J., MARSTEN, R. E., and SHANNO, D. F., Computational Experience with a Primal-Dual Interior-Point Method for Linear Programming, Linear Algebra and Its Applications, Vol. 152, pp. 191-222, 1991.
9. 9. YANG, D., and ZENIOS, S. A., A Scalable Parallel Interior-Point Algorithm for Stochastic Linear Programming and Robust Optimization, Computational Optimization and Applications, Vol. 7, pp. 143-158, 1997.
10. 10. DURAZZI, C., and GALLIGANI, E., Nonlinear Programming Methods for Solving Optimal Control Problems, Equilibrium Problems and Variational Models, Edited by F. Giannessi, A. Maugeri, and P. M. Pardalos, Kluwer Academic Publishers, Dordrecht, Netherlands (to appear).
11. 11. WETS, R. J. B., Stochatistic Programming, Handbook in Operation Research and Management Science, Edited by G. L. Nemhauser, A. H. G. Rinnoy Kan, and M. J. Todd, North Holland, Amsterdam, Netherlands, Vol. 1, pp. 573-629, 1989.
12. 12. MULVEY, J. M., VANDERBEI, R. J., and ZENIOS S. A., Robust Optimization of Large-Scale Systems, Operations Research, Vol. 43, pp. 264-281, 1995.
13. 13. BERALDI, P., GRANDINETTI, L., MUSMANNO, R., and TRIKI, C., Parallel Algorithms to Solve Two-Stage Stochastic Linear Programs with Robustness Constraints, Parallel Computing, Vol. 26, pp. 1889-1908, 2000.
14. 14. DUFF, I. S., ERISMAN, A. M., and REID, J. K., Direct Methods for Sparse Matrices, Clarendon Press, Oxford, England, 1989.
15. 15. CARPENTER, T. J., and VANDERBEI, R. J., Symmetric Indefinite Systems for Interior-Point Methods, Mathematical Programming, Vol. 58, pp. 1-32, 1993.
16. 16. WRIGHT, S., Primal-Dual Interior-Point Methods, SIAM, Philadelphia, Pennsylvania, 1997.
17. 17. ZHANG, Y., Solving Large-Scale Linear Programs by Interior-Point Methods under the Matlab Environment, Technical Report TR 96-01, Department of Mathematics and Statistics, University of Maryland at Baltimore County, Baltimore, Maryland, 1996.
18. 18. LIU, J. W., NG, E. G., and PEYTON B. W., On Finding Supernodes for Sparse Matrix Computations, SIAM Journal on Matrix Analysis and Applications, Vol. 1, pp. 242-252, 1993.
19. 19. BERTSEKAS, D. P., and TSITSIKLIS, J. N., Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs, New Jersey, 1989.
20. 20. THE MPI COMMITTEE, MPI: A Message-Passing Interface Standard, University of Tennessee, Knoxville, Tennessee, 1995.
21. 21. BARVIRUSO, R., and KNIES, A., SHMEM Technical Notes for Fortran, Cray Research, Seattle, Washington, 1994.
22. 22. KOJIMA, M., MEGIDDO, N., and MIZUNO, S., A Primal - Dual Infeasible-Interior-Point Algorithm for Linear Programming, Mathematical Programming, Vol. 61, pp. 263-280, 1993.
23. 23. EISENSTAT, S. C., and WALKER, H. F., Choosing the Forcing Terms in an Inexact Newton Method, SIAM Journal on Scientific Computing, Vol. 17, pp. 16-32, 1996.
24. 24. HOLMES, D., A Collection of Stochastic Programming Problems, Technical Report TR 94-11, University of Michigan, Ann Arbor, Michigan, 1994.
25. 25. HO, J. R., and LOUTE, E., A Set of Staircase Linear Programming Test Problems, Mathematical Programming, Vol. 20, pp. 245-250, 1981.
26. 26. MEHROTRA, S., On the Implementation of a Primal - Dual Interior-Point Method, SIAM Journal on Optimization, Vol. 2, pp. 575-601, 1992.