Bibliography

This bibliography lists the publications that you may need to use with the Optimization Library and describes how to obtain them.

Publications are listed by the author's name. References to IBM publications that include an order number, other than an IBM Technical Report, can be ordered through the Subscription Library Services System (SLSS). The non-IBM publications listed here should be obtained through publishers, bookstores, or professional computing organizations. 

References

Textbooks and articles covering the mathematical aspects of the library are listed in this section. The books by Dantzig, Beale, and Chvatal are fundamental references. All these books and articles can be used as sources of additional reading on related topics. They are listed alphabetically.

Each citation in the text of this book is shown as a number enclosed in square brackets. It indicates the number of the item listed below. For example, reference [1] cites the first item listed below.

  1. Anbil, R., Tanga, R., and Johnson, E. L. "A Global Approach to Crew-Pairing Optimization." IBM Systems Journal, Volume 31, No. 1, 71-78 (1992).
  2. Barr, R.; Glover, F.; Klingman, D. "Enhancements of Spanning Tree Labeling Procedures for Network Optimization." INFOR 17, 16-34 (1979).
  3. Beale, E. M. L. "Advanced Algorithmic Features for General Mathematical Programming Systems." Integer and Nonlinear Programming, ed. J. Abadie, 119-37. Amsterdam: North-Holland, 1970.
  4. Beale, E. M. L. Introduction to Optimization. New York: John Wiley & Sons, 1988.
  5. Beale, E. M. L. Mathematical Programming in Practice. London: Pitman, 1968.
  6. Beale, E. M. L., and Tomlin, J. A. "Special Facilities in a General Mathematical Programming System for Non-Convex Problems Using Ordered Sets of Variables." Proceedings 5th IFORS Conference, ed. J. Lawrence. London: Tavistock, 1970.
  7. Benichou, M.; Gauthier, J. M.; Girodet, P.; Hentges, G.; Ribiere, G.; and Vincent, D. "Experiments in Mixed Integer Linear Programming." Mathematical Programming 1, 76-94 (1971).
  8. Bradley, S. P.; Hax, A. C.; and Magnanti, T. L. Applied Mathematical Programming. Reading, Massachusetts: Addison-Wesley, 1977.
  9. Chinneck, J.W. "Computer Codes for the Analysis of Infeasible Linear Programs." Journal of the Operational Research Society, Volume 47, 61-72 (1996).
  10. Chinneck, J.W. "MINOS(IIS): Infeasibility Analysis Using MINOS." Computers and Operations Research, Volume 21, No. 1, 1-9 (1994).
  11. Chinneck, J.W., and Dravnieks, E.W. "Locating Minimal Infeasible Constraint Sets in Linear Programs." ORSA Journal on Computing, Volume 3, No. 2, 157-168 (1991).
  12. Chvatal, V. Linear Programming. New York: W. H. Freeman and Co., 1983.
  13. Crowder, H.; Johnson, E. L.; Padberg, M. W. "Solving Large Scale Zero-One Linear Programming Problems." Operations Research 31, 803-34 (1983).
  14. Dantzig, G. B. Linear Programming and Extensions. Princeton, New Jersey: Princeton University Press, 1963.
  15. Duncan, R. Extending DOS. New York: Addison-Wesley, 1990.
  16. Fletcher, R. Practical Methods of Optimization. New York: John Wiley & Sons, 1987.
  17. Forrest, J. J. H.; Hirst, J. P. H.; and Tomlin, J. A. "Practical Solution of Large Mixed Integer Programming Problems with UMPIRE." Management Science 20, (1974).
  18. Forrest, J. J. H., and Tomlin, J. A. "Implementing Interior Point Linear Programming Methods for the Optimization Subroutine Library." IBM Systems Journal, Volume 31, No. 1, 26-38 (1992).
  19. Forrest, J. J. H., and Tomlin, J. A. "Implementing the Simplex Method for the Optimization Subroutine Library." IBM Systems Journal, Volume 31, No. 1, 11-25 (1992).
  20. Forrest, J. J. H., and Tomlin, J. A. "Updating the Triangular Factors of the Basis to Maintain Sparsity in the Product Form Simplex Method." Mathematical Programming 2, 263-78 (1972).
  21. Forrest, J. J. H., and Tomlin, J. A. "Vector Processing in Simplex and Interior Methods for Linear Programming." Annals of Operations Research 22, 71-100 (1990).
  22. George, Alan, and Liu, Joseph W-H. "Computer Solution of Large Sparse Positive Definite Systems." Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1981.
  23. Gill, P. E.; Murray, W.; Saunders, M. A.; Tomlin, J. A.; and Wright, M. H. "On Projected Newton Barrier Methods for Linear Programming and an Equivalence to Karmarkar's Projective Method." Mathematical Programming 36, 183-209 (1986).
  24. Gill, P. E.; Murray, W.; Saunders, M. A.; and Wright, M. H. "A Practical Anti-Cycling Procedure for Linear and Nonlinear Programming." Technical Report, Department of Operations Research, Stanford University, Palo Alto, California, 1988.
  25. Goldfarb, D., and Idnani, A. "A Numerically Stable Dual Method for Solving Strictly Convex Quadratic Programs." Mathematical Programming 27, 1-33 (1983).
  26. Goldfarb, D., and Reid, J. K. "A Practicable Steepest-Edge Simplex Algorithm." Mathematical Programming 12, 361-71 (1977).
  27. Grigoriadis, M. "An Efficient Implementation of the Network Simplex Method." Mathematical Programming Study 26, 83-111 (1984).
  28. Guingnard, M.; Spielberg, K.; and Suhl, U. "Survey of Enumerative Methods for Integer Programming." Proceedings of SHARE, ACM. 1978.
  29. Guingnard, M., and Spielberg, K. "Logical Reduction Methods in Zero-One Programming Minimal Preferred Variables." Journal of ORSA. Volume 29, 1981.
  30. Gupta, Anshul, "Graph Partitioning Based Sparse Matrix Orderings for Interior-Point Algorithms," IBM Research Report RC 20467 (90480), May, 1996. T.J. Watson Research Center, Yorktown Hgts., NY.
  31. Harris, Paula M. J. "Pivot Selection Methods of the Devex LP Code." Mathematical Programming 5, 1-28 (1973).
  32. Hung, M. S., Rom, W. O., and Waren, A.D. Optimization Using IBM OSL. Danvers, Massachusetts: Boyd and Fraser, 1994.
  33. Jensen, D. L., and King, A. J. "A Decomposition Method for Quadratic Programming." IBM Systems Journal, Volume 31, No. 1, 39-48 (1992).
  34. Jensen, D. L., and King, A. J. "Frontier: A Graphical Interface for Portfolio Optimization in a Piecewise Linear-Quadratic Risk Framework." IBM Systems Journal, Volume 31, No. 1, 62-70 (1992).
  35. Johnson, E. L., and Nemhauser, G. L. "Recent Developments and Future Directions in Mathematical Programming." IBM Systems Journal, Volume 31, No. 1, 79-93 (1992).
  36. Karmarkar, N. "A New Polynomial-Time Algorithm for Linear Programming." Proceedings of the 16th Annual ACM Symposium on the Theory of Computing. 1984.
  37. Kennington, J., and Helgason, R. Algorithms for Network Flow Programming. New York: John Wiley & Sons, 1980.
  38. Land, A. H., and Doig, A. G. "An Automatic Method of Solving Discrete Programming Problems." Econometrica 28, 497-520 (1960).
  39. Lustig, I. J.; Marsten, R. E.; and Shanno, D. F. "Computational Experience with a Primal-Dual Interior Point Method for Linear Programming." Technical Report SOR 89-17, Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey, 1989. (To appear in Linear Algebra and its Applications.)
  40. Lustig, I. J.; Marsten, R. E.; and Shanno, D. F. "On Implementing Mehrotra's Predictor-Corrector Interior Point Method for Linear Programming." Technical Report SOR 90-03, Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey, 1990.
  41. Megiddo, N. "Pathways to the Optimal Set in Linear Programming." Progress in Mathematical Programming: Interior-Point and Related Methods, ed. N .Megiddo. Springer-Verlag, New York, 1989.
  42. Mehrotra, S. "On the Implementation of a (Primal-Dual) Interior Point Method." Technical Report 90-03, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois, 1990.
  43. Minkoff, A. S. "A Systematic Approach to OSL Application Programming." IBM Systems Journal, Volume 31, No. 1, 49-61 (1992).
  44. Murty, K. G. Linear and Combinatorial Programming. New York: John Wiley & Sons, 1976.
  45. Paige, C. C., and Saunders, M. A. "Solution of Sparse Indefinite Systems of Linear Equations." SIAM Journal on Numerical Analysis 12, 617-29 (1975).
  46. Paige, C. C., and Saunders, M. A. "LSQR: An Algorithm for Sparse Linear Equations and Sparse Least-Squares." ACM Transactions on Mathematical Software 8, 43-71 (1982).
  47. Saunders, M. A., and Tomlin, J. A., "Solving Regularized Linear Programs Using Barrier Methods and KKT Systems", IBM Research Report RJ 10064, and Stanford SOL Report 96-4, December 1996.
  48. Schrijver, A. Theory of Linear and Integer Programming. New York: John Wiley & Sons, 1987.
  49. Suhl, U. H., and Aittoniemi, L. "Computing Sparse LU-Factorization for Large-Scale Linear Programming Bases." Arbeitpaper Number 58/57, Fachbereich Wirtschaftswissenschaft, Angewandte Informatik. Frie Universitaet Berlin, 1987.
  50. Tomlin, J. A. "Branch and Bound Methods for Integer and Non-Convex Programming." Integer and Non-Linear Programming, ed. J. Abadie. Amsterdam: North-Holland, 1970.
  51. Tomlin, J. A. "A Note on Comparing Simplex and Interior Methods for Linear Programming" Progress in Mathematical Programming, ed. N. Megiddo. New York: Springer-Verlag, 1989.
  52. UMPIRE Users' Guide. London: Scientific Control Systems Ltd., 1970.
  53. Wilson, D. G., and Rudin, B.D. "Introduction to the Optimization Subroutine Library." IBM Systems Journal, Volume 31, No. 1, 4-10 (1992).
  54. Winston, Wayne L. Operations Research--Applications and Algorithms Boston, Massachusetts: PWA-Kent Publishing Company, 1991.
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