ABS methods and ABSPACK for linear systems and optimization: A review

4OR

Volumn 1, Issue 1, 2003, Pages 51-66

  Spedicato, Emilio ^a   Bodon, Elena ^a   Del Popolo, Antonino ^a   Mahdavi Amiri, Nezam ^b  

^a UNIVERSITY OF BERGAMO   (Italy)

^b SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

ABS methods; ABSPACK; Diophantine equations; feasible direction methods; linear algebraic systems; simplex method

Indexed keywords

EID: 4544324179     PISSN: 16194500     EISSN: 16142411     Source Type: Journal    
DOI: 10.1007/s10288-002-0004-0     Document Type: Article

References (25)

1. Abaffy J, Spedicato E (1989) ABS Projection Algorithms: Mathematical Techniques for Linear and Nonlinear Equations, Ellis Horwood, Chichester.
2. Abaffy J, Broyden CG, Spedicato E (1984) A class of direct methods for linear systems, Numerische Mathematik 45: 361-376.
3. Bertrand I, Betti G (1850) Traité élémentaire d' algèbre.
4. Bodon E (1993) Numerical experiments with ABS algorithms on banded systems of linear equations, Report CERFACS TR/PA/93/13, Toulouse.
5. Bodon E, Spedicato E, Luksan L (2000a) Computational experience withABSalgorithms for determined and underdetermined linear systems, Report DMSIA 00/21, University of Bergamo.
6. Bodon E, Spedicato E, Luksan L (2000b) Computational experience with ABS algorithms for overdetermined linear systems, Report DMSIA 00/19, University of Bergamo.
7. Bodon E, Spedicato E, Luksan L (2000c) Computational experience with ABS algorithms for KKT linear systems, Report DMSIA 00/20, University of Bergamo.
8. Egervary E (1955) Auflösung eines homogenen linearen diophantischen Gleichungsystems mit Hilfe von Projektormatrizen, Publ Math Debrecen 4: 481-483.
9. Esmaeili H, Mahdavi-Amiri, Spedicato E (2000) Explicit ABS solution of a class of linear inequality systems and LP problems, Report DMSIA 2/01, University of Bergamo.
10. Esmaeili H, Mahdavi-Amiri N, Spedicato E (2001a) Solution of Diophantine linear systems via the ABS methods, Numerische Mathematik 90: 101-115.
11. Esmaeili H, Mahdavi-Amiri N, Spedicato E (2001b)ABS solution of a class of linear integer inequalities and integer LP problems, Optimization Methods and Software 16: 179-202.
12. Esmaeili H, Mahdavi-Amiri N, Spedicato E (2001c) Generating the integer null space and conditions for determination of an integer basis using the ABS algorithms, Bulletin of the Iranian Mathematical Society 27: 1-18.
13. Feng E, Xia Z, Zhang L (1998) Introduction to ABS methods in optimization, Dalian University Press.
14. Forrest JJH, GoldfarbD (1992) Steepest edge simplex algorithms for linear programming, Mathematical Programming 57: 341-374.
15. Mirnia K (1996) Numerical experiments with iterative refinement of solutions of linear equations by ABS methods, Report DMSIA 32/96, University of Bergamo.
16. Rosser JB (1941) A note on the linear Diophantine equation, Amer Math Monthly 48, 662-666.
17. Schrijver A (1986) Theory of Linear and Integer Programming, JohnWiley and Sons.
18. Spedicato E, Li Z (2000) On some classes of iterative ABS-like methods for large scale linear systems. In: Brugnano L, Trigiante D (eds) Recent Trends in Numerical Analysis, Nova Scientia Publ. Inc, pp 329-344.
19. Spedicato E, Zhao J (1993) Explicit general solution of the Quasi-Newton equation with sparsity and symmetry, Optimization Methods and Software 2: 311-319.
20. Spedicato E, Xia Z, Zhang L (1997) The implicit LX method of the ABS class, Optimization Methods and Software 8: 99-110.
21. Spedicato E, Xia Z (1999) ABS formulation of Fletcher implicit LU method for factorizing a matrix and solving linear equations and LP problems, Report DMSIA 99/1, University of Bergamo.
22. Spedicato E, Bodon E, Del Popolo A, Xia Z (2000)ABS algorithms for linear systems and optimization: a review and bibliography, Ricerca Operativa 29: 39-88.
23. Zhang L (1995) Updating of Abaffian under perturbation in W and A, Report DMSIA 95/15, University of Bergamo.
24. Zhang L (1997) On an ABS algorithm with singular initial matrix and its application to linear programming, Optimization Methods and Software 8: 143-156.
25. Zhang L, Xia Z (1995) Application of the implicit LX method to linear programming, Report DMSIA 95/9, University of Bergamo.