Algorithms for the frame of a finitely generated unbounded polyhedron

INFORMS Journal on Computing

Volumn 18, Issue 1, 2006, Pages 97-110

  Dulá, José H ^a   López, Francisco J ^b  

^a VIRGINIA COMMONWEALTH UNIVERSITY   (United States)

^b UNIVERSITY OF TEXAS AT EL PASO   (United States)

Author keywords

Convex analysis; Extreme points and rays; Linear programming

Indexed keywords

EID: 33645559043     PISSN: 10919856     EISSN: 15265528     Source Type: Journal    
DOI: 10.1287/ijoc.1040.0109     Document Type: Review

References (27)

1. Akhavein, J. D., A. N. Berger, D. B. Berger. 1997. The effects of megamergers on efficiency and prices: Evidence from a bank profit function. Rev. Indust. Organ. 12 95-139.
2. Application Development Tools. 1994. IMSL Stat Library. Visual Numerics, Inc., Houston, TX.
3. Barnet, V. 1976. The ordering of multivariate data. J. Roy. Statist. Soc. A 139, Part 3 318-344.
4. Berger, A. N., L. J. Mester. 1997. Inside the black box: What explains differences in the efficiencies of financial institutions. J. Banking Finance 21 895-947.
5. Berger, A. N., D. Hancock, D. B. Humphrey. 1993. Bank efficiency derived from the profit function. J. Banking Finance 17 317-347.
6. Chan, T. M. 1996. Output-sensitive results on convex hulls, extreme points, and related problems. Discrete Comput. Geometry 16 369-387.
7. Clarkson, K. L. 1994. More output-sensitive geometric algorithms. Proc. 35th IEEE Sympos. Foundations Comput. Sci., Santa Fe, NM, 695-702.
8. Dulá, J. H. 1994. Geometry of optimal value functions with applications to redundancy in linear programming. J Optim. Theory Appl. 81 35-52.
9. Dulá J. H., R. V. Helgason. 1996. A new procedure for identifying the frame of the convex hull of a finite collection of points in multidimensional space. Eur. J. Oper. Res. 92 352-367.
10. Dulá, J. H., R. M. Thrall. 2001. A computational framework for accelerating DEA. J. Productivity Anal. 16 63-78.
11. Dulá, J. H., R. V. Helgason, B. L. Hickman. 1992. Preprocessing schemes and a solution method for the convex hull problem in multidimensional space. O. Balci, ed. Computer Science and Operations Research: New Developments in Their Interfaces. Pergamon Press, UK, 59-70.
12. Dulá, J. H., R. V. Helgason, N. Venugopal. 1997. An algorithm for identifying the frame of a pointed finite conical hull. INFORMS J, Comput. 10 323-330.
13. Edelsbrunner, H. 1987. Algorithms in combinatorial geometry. Monographs in Theoretical Computer Science, Vol. 10. Springer-Verlag, New York.
14. Federal Financial Institutions Examination Council. 2004. 2004 Report of Condition and Income. www.chicagofed.org/economic_research_and_data/ commercial_bank_data.cfm. Retrieval date: February 6, 2004.
15. Fukuda, K. 2004. Frequently asked questions in polyhedral computation. http://www.cs.mcgill.ca/~fukuda/soft/polyfaq/. Retrieval date: June 18, 2004.
16. Gerstenhaber, M. 1951. Theory of convex polyhedral cones. T. C. Koopmans, ed. Activity Analysis of Production and Allocation. Chapman and Hall, London, UK, 298-316.
17. Graham, R., F. Yao. 1990. A whirlwind tour of computational geometry. Amer. Math. Monthly 97 687-701.
18. López, F. J. 1999. Algorithms to obtain the frame of a finitely generated unbounded polyhedron. Unpublished doctoral dissertation, School of Business Administration, University of Mississippi, University, MS.
19. Mattheiss, T. H., D. S. Rubin. 1980. A survey and comparison of methods for finding all vertices of convex polyhedral sets. Math. Oper. Res. 5 167-185.
20. Ottmann, T., S. Schuierer, S. Soundaralakshimi. 1995. Enumerating extreme points in higher dimension. Proc. 12th Annual Sympos. Theoret. Aspects Comput. Sci., LNCS, Vol. 900. Springer, Berlin, Germany, 562-570.
21. Ottmann, T., S. Schuierer, S. Soundaralakshimi. 2001. Enumerating extreme points in higher dimension. Nordic J. Comput. 8 179-192.
22. Preparata, F. P., M. I. Shamos. 1985. Computational Geometry: An Introduction. Springer-Verlag, New York.
23. Reay, J. R. 1965. Generalizations of a theorem of Carathéodory. Memoirs Amer. Math. Soc. 54 1-50.
24. Rockafellar, R. T. 1970. Convex Analysis. Princeton University Press, Princeton, NJ.
25. d. P. M. Pardalos, ed. Advnces in Optimization and Parallel Computing. North Holland, Amsterdam, The Netherlands, 267-292.
26. Wallace, S. W., R. J.-B. Wets. 1992. Preprocessing in stochastic programming: The case of linear programs. ORSA J. Comput. 4 45-59.
27. Wets, R. J.-B., C. Witzgall. 1967. Algorithms for frames and lineality spaces of cones. j. Res. National Bureau Standards Sect. B. Math. Math. Phys. 71B 1-7.