Direct solution of linear systems of size 109 arising in optimization with interior point methods

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3911 LNCS, Issue , 2006, Pages 513-525

  Gondzio, Jacek ^a   Grothey, Andreas ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ITERATIVE METHODS; LINEAR EQUATIONS; MATRIX ALGEBRA; OBJECT ORIENTED PROGRAMMING; PARALLEL PROCESSING SYSTEMS; PROBLEM SOLVING;

BLOCK STRUCTURES; INTERIOR POINT METHODS; OPTIMIZER; PARALLEL ARCHITECTURE;

LINEAR SYSTEMS;

EID: 33745801596     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11752578_62     Document Type: Conference Paper

References (15)

1. Karmarkar, N.K.: A new polynomial-time algorithm for linear programming. Combinatorica 4 (1984) 373-395
2. Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia (1997)
3. Andersen, E.D., Gondzio, J., Mészáros, C., Xu, X.: Implementation of interior point methods for large scale linear programming. In Terlaky, T., ed.: Interior Point Methods in Mathematical Programming. Kluwer Acad Pub (1996) 189-252
4. Altman, A., Gondzio, J.: Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization. Optimization Methods and Software 11-12 (1999) 275-302
5. Gondzio, J., Sarkissian, R.: Parallel interior point solver for structured linear programs. Mathematical Programming 96(3) (2003) 561-584
6. Gondzio, J., Grothey, A.: Parallel interior point solver for structured quadratic programs: Application to financial planning problems. Technical Report MS-03-001, School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland, UK (2003) Accepted for publication in Annals of Operations Research.
7. Gondzio, J., Grothey, A.: Exploiting structure in parallel implementation of interior point methods for optimization. Technical Report MS-04-004, School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland, UK (2004)
8. Gondzio, J., Grothey, A.: Solving nonlinear portfolio optimization problems with the primal-dual interior point method. Technical Report MS-04-001, School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland, UK (2004) Accepted for publication in European Journal of Operational Research.
9. Ziemba, W.T., Mulvey, J.M.: Worldwide Asset and Liability Modeling. Publications of the Newton Institute. Cambridge University Press, Cambridge (1998)
10. Arioli, M., Duff, I.S., de Rijk, P.P.M.: On the augmented system approach to sparse least-squares problems. Numerische Mathematik 55 (1989) 667-684
11. Duff, I.S., Erisman, A.M., Reid, J.K.: Direct methods for sparse matrices. Oxford University Press, New York (1987)
12. Vanderbei, R.J.: Symmetric quasidefinite matrices. SIAM Journal on Optimization 5 (1995) 100-113
13. Konno, H., Shirakawa, H., Yamazaki, H.: A mean-absolute deviation-skewness portfolio optimization model. Annals of Operational Research 45 (1993) 205-220
14. Markowitz, H.M.: Portfolio selection. Journal of Finance (1952) 77-91
15. Steinbach, M.: Markowitz revisited: Mean variance models in financial portfolio analysis. SIAM Review 43(1) (2001) 31-85