An interior multiobjective primal-dual linear programming algorithm based on approximated gradients and efficient anchoring points

Computers and Operations Research

Volumn 24, Issue 4, 1997, Pages 353-365

  Arbel, Ami ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; DECISION MAKING; ITERATIVE METHODS; LINEAR PROGRAMMING;

MULTIPLE CRITERIA DECISION MAKING (MCDM); MULTIPLE OBJECTIVE LINEAR PROGRAMMING (MOLP) PROBLEMS;

OPERATIONS RESEARCH;

EID: 0031119489     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0305-0548(96)00055-X     Document Type: Article

References (16)

1. Steuer, R. E., Multiple Criteria Optimization: Theory, Computation, and Application. Wiley, New York, 1986.
2. Zeleny, M., Multiple Criteria Decision Making. McGraw-Hill, 1982.
3. Karmarkar, N. K., A new polynomial time algorithm for linear programming. Combinatorica, 1984, 4, 373-395.
4. Cheng, Y.-C., Houck, D. J., Liu, J.-M., Meketon, M. S., Slutsman, L., Vanderbei, R. J. and Wang, P., The AT & T KORBX ® system. AT & T Tech. J., 1989, 68, 3 7-19.
5. Kojima, M., Mizuno, S. and Yoshise, A., A primal-dual interior point algorithm for linear programming. In Progress in Mathematical Programming, Interior-Point and Related Method, ed. N. Megiddo, pp. 29-48, Springer-Verlag, Berlin, 1989.
6. Marsten, R. E., Saltzman, M. J., Shanno, D. F., Pierce, G. S. and Ballintijn. J. F., Implementation of a dual affine interior point algorithm for linear programming. ORSA J. Comp., 1989, 1, 4 287-297.
7. McShane, K. A., Monma, C. L. and Shanno, D. F., An implementation of a primal-dual interior point method for linear programming. ORSA J. Comp., 1989, 1, 2 70-83.
8. Megiddo, N., Progress in Mathematical Programming: Interior-Point and Related Methods, Springer-Verlag, Berlin, 1989.
9. Monma, C. L. and Morton, A. J., Computational experience with a dual variant of Karmarkar's method for linear programming. Opns Res. Letts, 1987, 6, 6 261-267.
10. Vanderbei, R. J., Meketon, M. S. and Freedman, B. A., A modification of Karmarkar's linear programming algorithm. Algorithmica, 1986, 1, 395-407.
11. Kranich, E., Interior point methods for mathematical programming: a bibliography. Discussion Paper, No. 171, May 1991, Institute of Economy and Operations Research, Fern Universität Hagen, Germany, 1991.
12. Gill, P. E., Murray, W. and Saunders, M. A., Interior-point methods for linear programming: A challenge to the simplex method. Technical Report SOL 88-14, Department of Operations Research, Stanford University, 1988.
13. Arbel, A., An interior multiobjective linear programming algorithm. Comp. Opns Res., 1993, 20, 7 723-735.
14. Saaty, T. L., Multicriteria Decision Making: The Analytic Hierarchy Process. RSW Publications, Pittsburgh, PA, 1988.
15. Arbel, A., Exploring Interior-Point Linear Programming: Algorithms and Software. MIT Press, Cambridge, MA, 1993.
16. Arbel, A., Anchoring points and cones of opportunities in interior multiobjective linear programming problems. J. Opl Res. Soc., 1994, 45, 1 83-96.