An efficient simplex type algorithm for sparse and dense linear programs

European Journal of Operational Research

Volumn 148, Issue 2, 2003, Pages 323-334

  Paparrizos, Konstantinos ^a   Samaras, Nikolaos ^a   Stephanides, George ^a  

^a UNIVERSITY OF MACEDONIA   (Greece)

Author keywords

Algorithm evaluation; Big M method; Linear programming; Numerical experiments; Simplex type algorithms

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; ITERATIVE METHODS; LINEAR PROGRAMMING; PROBLEM SOLVING;

EXTERIOR POINT SIMPLEX ALGORITHMS (EPSA);

OPERATIONS RESEARCH;

EID: 0037449234     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(02)00400-9     Document Type: Article

References (28)

1. Alexouda G., Paparrizos K. A comparative computational study with an exterior point simplex algorithm. Proceedings of 4th Balkan Conference on Operational Research. 1:1997;12-22.
2. Anstreicher G., Terlaky T. A monotonic build-up simplex algorithm for linear programming. Operation Research. 42:1994;556-561.
3. Avis D., Chvatal V. Notes on Bland's pivoting rule. Mathematical Programming Study. 8:1978;24-34.
4. Bixby R.E. Progress in linear programming. ORSA journal of computing. 6(1):1994;15-22.
5. Borgwardt K.H. The simplex method: A probabilistic analysis. Algorithms and Combinatorics. vol. 1:1987;Springer Verlag.
6. Cardoso D., Climaco J. The generalized simplex method. Operations Research Letters. 12(5):1992;337-348.
7. Chen H., Pardalos P., Saunders M. The simplex algorithm with a new primal and dual pivot rule. Operations Research Letters. 16:1994;121-127.
8. Dosios K., Paparrizos K. Resolution of the problem of degeneracy in a primal and dual simplex algorithm. Operation Research Letters. 20:1997;45-50.
9. Eisenstat S.C., Schultz M.H., Sherman A.H. Algorithms and data structures for sparse symmetric Gaussian elimination. SIAM Journal on Scientific and Statistical Computing. 2:1981;225-237.
10. Forrest J.J.H., Goldfarb D. Steepest-edge simplex algorithms for linear programming. Mathematical Programming. 57:1992;341-374.
11. J.R. Gilbert, C. Moler, R. Schreiber, Sparse matrices in MATLAB: Design and implementation, Technical Paper CS1 91-4, Xerox Palo Alto Research Center, 1990.
12. Gill P., Murray W., Saunders M., Wright M. Sparse matrix methods in optimization. SIAM Journal on Scientific and Statistical Computing. 5(3):1984;562-589.
13. Goldfarb D., Sit W.Y. Worst case behavior of the steepest edge simplex method. Discrete Applied Mathematics. 1:1979;277-285.
14. Gondzio J. Another simplex type method for large scale linear programming. Control and Cybernetics. 25(4):1996;739-760.
15. Klee V., Minty G.J. How good is the simplex algorithm. Shisha O. Inequalities III. 1972;158-172 Academic Press, New York.
16. Mitra G., Tamiz M., Yadegar J. Experimental investigation of an interior search method within a simplex framework. Communications of ACM. 31:1988;1474-1482.
17. Paparrizos K. Pivoting rules directing the Simplex method through all feasible vertices of Klee-Minty examples. Operations Research. 26:1989;77-95.
18. K. Paparrizos, A generalization of an exterior point simplex algorithm for linear programming problems, Technical Report, University of Macedonia, 1990.
19. Paparrizos K. An infeasible exterior point simplex algorithm for assignment problems. Mathematical Programming. 51:1991;45-54.
20. Paparrizos K. An exterior point simplex algorithm for general linear problems. Annals of Operation Research. 32:1993;497-508.
21. Paparrizos K. Exterior point simplex algorithm: Simple and short proof of correctness. Proceedings of SYMOPIS'96. 1996;13-18.
22. K. Paparrizos, N. Samaras, K. Tsiplidis, Pivoting algorithms for (LP) generating two paths, in: M.P. Pardalos, A.C. Floudas (Eds.), Encyclopedia of Optimization, vol. 4, Kluwer Academic Publishers, 2001, pp. 302-306.
23. Park S.K., Miller K.W. Random number generators: Good ones are hard to find. Communications of the ACM. 32(10):1988;1192-1201.
24. Roos C. An exponential example for Terlaky's pivoting rule for the Criss-cross Simplex method. Mathematical Programming. 46:1990;78-94.
25. Saad Y., Sosonkina M. Distributed Schur complement techniques for general sparse linear systems. SIAM Journal on Scientific and Statistical Computing. 21(4):1999;1337-1356.
26. Suhl U.H., Suhl L.M. Computing sparse LU factorization for large-scale linear programming bases. ORSA Journal on Computing. 2(4):1990;325-335.
27. Wolfe P. Methods for nonlinear programming. Graves R.L., Wolfe P. Recent Advances in Mathematical Programming. 1963;McGraw-Hill, New York.
28. Wolfe P., Culter L. Experiments in linear programming. Graves R.L., Wolfe P. Recent Advances in Mathematical Programming. 1963;177-200 McGraw-Hill, New York.