On duality in multiple objective linear programming

European Journal of Operational Research

Volumn 210, Issue 2, 2011, Pages 158-168

  Luc, Dinh The ^a  

^a UNIVERSITY OF AVIGNON   (France)

Author keywords

Duality; Multiple objective linear problem; Normal cone

Indexed keywords

CONVEX POLYHEDRAL; DUAL PROBLEM; DUALITY; DUALITY RELATIONS; GEOMETRIC DUALITY; MAXIMAL ELEMENTS; MULTIPLE OBJECTIVE LINEAR PROGRAMMING; MULTIPLE OBJECTIVES; NORMAL CONES; STRONG DUALITY; SUPPORT FUNCTIONS;

OPTIMIZATION;

EID: 78650415390     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2010.09.024     Document Type: Article

References (19)

1. A. Balbas, and A. Heras Duality theory for infinite dimensional multiobjective linear programming European Journal of Operations Research 68 1993 379 388 (Pubitemid 23680558)
2. A. Balbas, P. Jimenez, and A. Heras Duality theory and slackness conditions in multiobjective linear linear programming Computer and Mathematics with Applications 37 1999 101 109
3. H.W. Corley Duality theory for the matrix linear programming problem Journal of Mathematical Analysis and Applications 104 1984 47 52
4. G. Danzig Linear Programming and Extension 1963 Princeton New Jersey
5. E. Galperin, and J. Jimerez Guerra Duality of nonscalarized multiobjective linear programs: dual balance, level sets and dual clusters of optimal vectors Journal of Optimization Theory and Applications 108 2001 109 137 (Pubitemid 33383258)
6. F. Heyde, and A. Lohne Geometric duality in multiple objective linear programming SIAM Journal of Optimization 19 2008 836 845
7. F. Heyde, A. Lohne, and C. Tammer Set-valued duality theory for multiple objective linear programs and application to mathematical finance Mathematical Methods of Operation Research 69 2009 159 179
8. H. Isermann On some relations between a dual pair of multiple objective linear programs Zeitschrift fur Operations Research 22 1978 33 41
9. J. Jahn, Mathematical Vector Optimization in Partially Ordered Linear Spaces, Lang, Frankfurt, 1986.
10. J. Jahn Vector Optimization Theory Applications and Extensions 2004 Springer-Verlag Berlin
11. N.T.B. Kim, and D.T. Luc Normal cones to a polyhedral convex set and generating efficient faces in linear multiobjective programming Acta Mathematica Vietnam 25 2000 101 124
12. N.T.B. Kim, and D.T. Luc The Normal cone method in solving linear multiobjective problems Journal of Statistical Management System 5 2002 341 358
13. J. Kolumban, Dualität bei optimierunsaufgaben, in: Proceedings of the Conference on Constructive Theory of Functions, Akademiai Kiado, Budapest, 1969, pp. 261-265.
14. J.S.H. Kornbluth Duality, indifference and sensitivity analysis in multiple objective linear programming Operations Research Quaterly 25 1974 599 614
15. D.T. Luc Theory of Vector Optimization LNEMS vol. 319 1989 Springer-Verlag Berlin
16. D.T. Luc, and J. Jahn Axiomatic approach to duality in optimization Numerical Functional Analysis and Optimization 13 1992 305 326
17. J.-E. Martinez-Legaz Generalized convex duality and its economic applications. Handbook of generalized convexity and generalized monotonicity Nonconvex Optimization and Applications vol. 76 2005 Springer New York pp. 237-292
18. R.T. Rockafellar Convex Analysis 1970 Princeton New Jersey
19. W. Rodder A generalized saddlepoint theory; its application to duality theory for linear vector optimum problems European Journal of Operations Research 1 1977 55 59