A new approach to duality in vector optimization

References

• Borwein , J and Lewis , A . 2000 . Convex Analysis and Nonlinear Optimization , New York : Springer .
   Google Scholar
• Boţ , RI and Wanka , G . 2004 . An analysis of some dual problems in multiobjective optimization. I, II . Optimization , 53 ( 3 ) : 281 – 300 . 301–324
   Web of Science ®Google Scholar
• Breckner , WW . 1972 . Dualität bei optimierungsaufgaben in halbgeordneten topologischen Vektorräumen. I . Mathematical Revue d'Analyse Numerique et de Theorie de l'Approximation , 1 : 5 – 35 .
   Google Scholar
• Corley , HW . 1981 . Duality theory for maximizations with respect to cones . Journal of Mathematical Analysis and Applications , 84 : 560 – 568 .
   Web of Science ®Google Scholar
• Dolecki , S and Malivert , C . 1993 . General duality in vector optimization . Optimization , 27 ( 1–2 ) : 97 – 119 .
   Google Scholar
• Hamel , A . 2005 . Variational Principles on Metric and Uniform Spaces , Halle–Wittenberg : Martin–Luther–Universität . Habilitation thesis
   Google Scholar
• Hamel , A , Heyde , F , Löhne , A , Tammer , Chr and Winkler , K . 2004 . Closing the duality gap in linear vector optimization . Journal of Convex Analysis , 11 ( 1 ) : 163 – 178 .
   Web of Science ®Google Scholar
• Isermann , H . 1978 . On Some Relations between a Dual Pair of Multiple Objective Linear Programs . Z. Oper. Res. Ser. A , 22 : 33 – 41 .
   Google Scholar
• Jahn , J . 1983 . Duality in vector optimization . Mathematical Programming , 25 : 343 – 353 .
   Web of Science ®Google Scholar
• Jahn , J . 1986 . Mathematical Vector Optimization in Partially Ordered Linear Spaces , Frankfurt am Main–Bern–New York : Verlag Peter Lang .
   Google Scholar
• Jahn , J . 2004 . Vector Optimization. Theory, Applications, and Extensions , Berlin : Springer-Verlag .
   Google Scholar
• Löhne , A . 2004 . “ On conjugate duality in optimization with set relations ” . In Entscheidungstheorie und -praxis in Industrieller Produktion und Umweltforschung , Edited by: Geldermann , J and Treitz , M . Aachen : Shaker .
   Google Scholar
• Löhne , A . 2005 . Optimization with set relations , Halle–Wittenberg : Martin–Luther–Universität . PhD Thesis
   Google Scholar
• Löhne , A . 2005 . Optimization with set relations: Conjugate duality . Optimization , 54 ( 3 ) : 265 – 282 .
   Web of Science ®Google Scholar
• Luc , DT . 1988 . “ Lecture notes in economics and mathematical sciences ” . In Theory of Vector Optimization , 319 Berlin : Springer-Verlag .
   Google Scholar
• Nakayama , H . 1999 . “ Duality in multi-objective optimization ” . In Multicriteria Decision Making , Edited by: Gal , T , Stewart , TJ and Hanne , T . Boston/Dordrecht/London : Kluwer Academic Publishers . 3-1–3-29
   Google Scholar
• Nieuwenhuis , JW . 1980 . Supremal points and generalized duality . Math. Operationsforsch. Stat., Ser. Optimization , 11 : 41 – 59 .
   Google Scholar
• Pallaschke , D and Rolewicz , S . 1997 . Foundations of Mathematical Optimization, Convex Analysis without Linearity , Dordrecht, Boston, London : Kluwer Academic Publishers .
   Google Scholar
• Postolica , V . 1986 . A Generalization of Fenchel's Duality Theorem, Ann. Sc. Math. Quebec , 10 : 199 – 206 .
   Google Scholar
• Rockafellar , RT . 1970 . Convex Analysis , Princeton, N.J : Princeton University Press .
   Google Scholar
• Rockafellar , RT and Wets , RJ-B . 1998 . Variational Analysis , Berlin : Springer .
   Google Scholar
• Sawaragi , Y , Nakayama , H and Tanino , T . 1985 . Theory of Multiobjective Optimization, Mathematics in Science and Engineering , Vol. 176 , Orlando : Academic Press Inc. .
   Google Scholar
• Schönfeld , P . 1970 . Some Duality Theorems for the Non-linear Vector Maximum Problem . Unternehmensforschung , 14 : 51 – 63 .
   Google Scholar
• Song , W . 1998 . A generalization of Fenchel duality in set-valued vector optimization . Mathematical Methods of Operations Research , 48 : 259 – 272 .
   Web of Science ®Google Scholar
• Tammer , Chr . 1991 . Lagrange-Dualität in der Vektoroptimierung . Wiss. Z. Tech. Hochsch. Ilmenau , 37 ( 3 ) : 71 – 88 .
   Google Scholar
• Tanino , T . 1988 . On the supremum of a set in a multi-dimensional space . Journal of Mathematical Analysis and Applications , 130 : 386 – 397 .
   Web of Science ®Google Scholar
• Tanino , T . 1992 . Conjugate duality in vector optimization . Journal of Mathematical Analysis and Applications , 167 ( 1 ) : 84 – 97 .
   Web of Science ®Google Scholar
• Tanino , T and Sawaragi , Y . 1979 . Duality theory in multiobjective programming . Journal of Optimization Theory and Applications , 27 : 509 – 529 .
   Web of Science ®Google Scholar