Convexity of the optimal multifunctions and its consequences in vector optimization

References

• Aubin , J.P and Ekeland , I . 1984 . Applied Nonlinear Analysis , New York : Jolln Wiley .
   Google Scholar
• Benson , A.P . 1983 . On a domination property for vector maximization with respect to cones . Journal of Optimization Theory and Applications , 39 : 125 – 132 . Errata Corrige, 43 (1984) 477-479
   Google Scholar
• Borwein , J.M . 1977 . Muitivaiued convexity and optimization: a unified approach inequality and equality constraints . Mathematical Programming , 13 : 183 – 199 .
   Web of Science ®Google Scholar
• Boewein , J.M . 1980 . The geometry of Pareto efficiency over cones . Math. Operationsforsch. Statist., Ser. Optimization , 11 : 235 – 248 .
   Google Scholar
• Borwein , J.M . 1987 . Automatic continuity and openness of convex relations . Proceedings of the American Mathematical Society , 99 : 49 – 55 .
   Google Scholar
• Choo , E.U and Chew , K.P . 1985 . Optimal value functions in parametric programming . Zeitschrift fur Operations Research , 29 : 47 – 57 .
   Google Scholar
• Fiacco , A.V and Kyparisis , J . 1986 . Convexity and concavity properties of the optimal value function in parametric nonlinear programming . Journal of Optimization Theory and Applications , 48 : 95 – 126 .
   Web of Science ®Google Scholar
• Hartley , R . 1978 . On cone efficiency, cone convexity and cone compactness . SIAM Journal on Applied Mathematics , 34 : 211 – 222 .
   Web of Science ®Google Scholar
• Hazen , G.B and Morin , T.L . 1983 . Optimally conditions in nonconical multiple-objective programming . Journal of Optimization Theory and Applications , 40 : 25 – 60 .
   Web of Science ®Google Scholar
• Henig , M.I . 1982 . Existence and characterization of efficient decisions with respect to cones . Mathematical Programming , 23 : 111 – 116 .
   Web of Science ®Google Scholar
• Klein , E and Thompson , A . 1984 . Theory of Correspondence , New York : John Wiley .
   Google Scholar
• Luc , D.T . 1984 . On the domination property in vector optimization . Journal of Optimization Theory and Applications , 43 : 327 – 330 .
   Web of Science ®Google Scholar
• Luc , D.T . 1984 . On duality theory in Multiobjective Programming . Journal of Optimization Theory and Application , 43 : 557 – 582 .
   Web of Science ®Google Scholar
• Nikodem , K . 1986 . Continuity of K-convex set-valued functions . Bulletin of the Polish Academy of Sciences Mathematics , 34 : 393 – 399 .
   Google Scholar
• Oettli , W . 1981 . “ Optimality conditions involving generalized convex mappings ” . In Generalized Concavity in Optimization and Economics , Edited by: Schaible , S and Ziemba , W.T . New York : Academic Press .
   Google Scholar
• Papageorgiou , N . 1986 . On the separation of closed convex sets , Vol. 27 , 221 – 228 . Mathematicae Universitatis Carolinae .
   Google Scholar
• Penot , J.P and Karwat , A . 1986 . Parametrized multicriteria optimization; continuity and closedness of optimal multifuntions . Journal of Mathematical Analysis and Applications , 120
   Google Scholar
• Penot , J.P and Sterna-Karwat , A . 1986 . Parametrized multicriteria optimization; order continuity of the marginal multifunctions . Journal of Mathematical Analysis and Applications , 120 to appear
   Google Scholar
• Robinson , S.M . 1976 . Regularity and stability for convex multivalued functions . Mathematics of Operations Research , 1 : 130 – 142 .
   Google Scholar
• Rockafellar , R.T . 1972 . Convex Analysis , Princeton, N.J : Princeton University Press .
   Google Scholar
• Rolewicz , S . 1979 . On ε-paraconvex multifunctions . Mathematics Japonica , 24 : 293 – 300 .
   Google Scholar
• Sawaragi , Y , Nakayam , H and Tanino , T . 1985 . Theory of Multiobjective Optimization , Academie Press .
   Google Scholar
• Sterna-Karwat , A . 1986 . On existence of cone-maximal points in real topological linear spaces . Israel Journal of Mathematics , 54 : 33 – 41 .
   Web of Science ®Google Scholar
• Sterna-Karwat , A . 1986 . A note on the solution set in optimization with respect to cones . Optimization , 17 : 297 – 303 .
   Google Scholar
• Sterna-Karwat , A . 1987 . A note on convex cones . Bull Austral Math Soc , 35 : 97 – 109 .
   Google Scholar
• Sterna-Karwat , A . 1987 . “ On the existence cone-efficient points ” . In Recent Advances and Historical Development of Vector Optimization , Edited by: Jahn , J and Krabs , W . 233 – 240 . Springer-Verlag .
   Google Scholar
• Yu , P.L . 1985 . Multiple Criteria Decision Making , New York : Plenum Press .
   Google Scholar