Simultaneous primal-dual right-hand-side sensitivity analysis from a strictly complementary solution of a linear program

SIAM Journal on Optimization

Volumn 10, Issue 2, 1999, Pages 427-442

  Greenberg, Harvey J ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

Computational economics; Interior point methods; Linear programming; Optimal partition; Parametric programming; Sensitivity analysis

Indexed keywords

EID: 0040196044     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/s1052623496310333     Document Type: Article

References (17)

1. I. ADLER AND R. MONTEIRO, A geometric view of parametric linear programming, Algorithmica, 8 (1992), pp. 161-176.
2. T. GAL, Postoptimal Analyses, Parametric Programming, and Related topics, 2nd ed., Walter de Gruyter, Berlin, Germany, 1995.
3. A. GOLDMAN AND A. TUCKER, Theory of linear programming, in Linear Inequalities and Related Systems, H. Kuhn and A. Tucker, eds., Ann. of Math. Stud. 38, Princeton University Press, Princeton, NJ, 1956, pp. 53-97.
4. H. GREENBERG, An analysis of degeneracy, Naval Res. Logist., 33 (1986), pp. 635-655.
5. H. GREENBERG, The use of the optimal partition in a linear programming solution for postoptimal analysis, Oper. Res. Lett., 15 (1994).
6. H. GREENBERG, Mathematical Programming Glossary, http://www.cudenver.edu/~hgreenbe/ glossary/glossary.html, 1996-9.
7. H. GREENBERG, Myths and Counterexamples in Mathematical Programming: LP-2, http:// www.cudenver.edu/~hgreenbe/myths/myths.html, 1996-9.
8. H. GREENBERG, Linear programming 1: Basic principles, in Recent Advances in Sensitivity Analysis and Parametric Programming, T. Gal and H. Greenberg, eds., Kluwer Academic Publishers, Boston, MA, 1997.
9. H. J. GREENBERG, A. G. HOLDER, K. ROOS, AND T. TERLAKY, On the dimension of the set of Rim perturbations for optimal partition invariance, SIAM J. Optim., 9 (1999), pp. 207-216.
10. B. JANSEN, C. ROOS, AND T. TERLAKY, An Interior Point Approach to Postoptimal and Parametric Analysis in Linear Programming, Report 92-21, Faculty of Technical Mathematics and Informatics/Computer Science, Delft University of Technology, Delft, The Netherlands, 1992.
11. H. MILLS, Marginal values of matrix games and linear programs, in Linear Inequalities and Related Systems, H. Kuhn and A. Tucker, eds., Ann. of Math. Stud. 38, Princeton University Press, Princeton, NJ, 1956, pp. 183-193.
12. H. MILLS, Marginal values of matrix games and linear programs, in Linear Inequalities and Related Systems, H. Kuhn and A. Tucker, eds., Ann. of Math. Stud. 38, Princeton University Press, Princeton, NJ, 1956, pp. 183-193.
13. R. D. C. MONTEIRO AND S. MEHROTRA, A general parametric analysis approach and its implication to sentitivity analysis in interior point methods, Math. Programming, 47 (1996), pp. 65-82.
14. C. ROOS, Interior point approach to linear programming: Theory, algorithms & parametric analysis, in Topics in Engineering Mathematics, A. van der Burgh and J. Simonis, eds., Kluwer Academic Publishers, Norwell, MA, 1992, pp. 181-216.
15. C. ROOS, T. TERLAKY, AND J.-P. VIAL, Theory and Algorithms for Linear Optimization: An Interior Point Approach, John Wiley, New York, 1996.
16. A. WILLIAMS, Marginal values in linear programming, J. Soc. Indust. Appl. Math., 11 (1963), pp. 82-94.
17. S. WRIGHT, Primal-Dual Interior-Point Methods, SIAM, Philadelphia, PA, 1997.