Connectivity of efficient solution sets in vector optimization of set-valued mappings

References

• Arrow , K.J. , Barankin , E.W. and Blackwell , D. “ Admissible points of convex sets, in Contributions to the Theory of Games, II ” . Edited by: Kuhn , H.W. 87 – 92 . Princeton, NJ : Princeton University Press .
   Google Scholar
• Aubin , J.P. and Ekeland , I. 1984 . “ Applied Nonlinear Analysis ” . New York : Wiley-Intersciences .
   Google Scholar
• Benson , H.P. 1979 . An improved definition of proper efficiency for vector minimization with respect to cone . J. Math. Anal. Appl. , 71 : 232 – 241 .
   Web of Science ®Google Scholar
• Bitran , G.R. and Magnanti , T.L. 1979 . The structure of admissible points with respect to cone dominance . J. Optim. Theory Appl , 29 : 573 – 614 .
   Web of Science ®Google Scholar
• Borwein , J.M. 1980 . The geometry of Pareto efficiency over cones . Math. Oper. Statist. Ser. Optim , 11 : 235 – 248 .
   Google Scholar
• Borwein , J.M. and Zhuang , D.M. 1993 . Super efficiency in vector optimization . Trans. Amer. Math. Soc , 338 : 105 – 122 .
   Web of Science ®Google Scholar
• Chen , G.Y. 1995 . Generalized Arrow-Barankin-Blackwell theorem in locally convex space . J. Optim. Theory and Appl , 84 : 93 – 101 .
   Google Scholar
• Dauer , J.P. and Gallagher , R.J. 1990 . Positive proper efficient points and related cone results in vector optimization theory . SIAM J. Control and Optim , 28 : 158 – 172 .
   Web of Science ®Google Scholar
• Engelking , R. 1977 . General Topology , Warszawa : Państwowe Wydawnictwo naukowe .
   Google Scholar
• Ferro , F. 1993 . A general form of the Arrow-Barankin-Blackwell theorem in normed space and the l∞ case . J. Optim. Theory and Appl , 79 : 127 – 138 .
   Google Scholar
• Gallagher , R.J. and Saleh , O.A. 1993 . Two generalization of a theorem of Arrow, Barankin and Blackwell . SIAM J. Control and Optim , 31 : 247 – 256 .
   Web of Science ®Google Scholar
• Gong , X.H. 1994 . Connectedness of efficient solutions sets for set-valued maps in normed spaces . J. Optim. Theory and Appl , 83 : 83 – 96 .
   Web of Science ®Google Scholar
• Gong , X.H. 1994 . Connectedness of the efficient solutions sets of a convex vector optimization in normed space . Nonlinear Analysis , 23 : 1105 – 1113 .
   Google Scholar
• Gong X. H. Connectedness of super efficient solution sets for set–valued maps – in Banach spaces (to appear in ZOR)
   Google Scholar
• Guerraggio , A. , Molho , E. and Zafferoni , A. 1994 . On the notion of proper efficiency in vector optimization . J. Optim. Theory, Appl , 82 : 1 – 21 .
   Web of Science ®Google Scholar
• Hartley , R. 1978 . On cone eficiency, cone convexity and cone compactness . SIAM J. Appl. Math , 34 : 211 – 222 .
   Web of Science ®Google Scholar
• Hiriart-Urruty , J.B. 1985 . Images of connected set by semicontinuous multifunctions . J. Math. Anal. Appl , 111 : 407 – 422 .
   Web of Science ®Google Scholar
• Holmes , R.B. 1975 . Geometric Functional Analysis and Its Applications , Springer-Verlag .
   Google Scholar
• Hu , Y.D. and Sun , E.J. 1993 . Connectedness of the efficient point set in strictly quasiconcave vector maximization . J. Optim. Theory and Appl , 78 : 613 – 622 .
   Web of Science ®Google Scholar
• Jahn , J. 1986 . “ Mathematical Vector Optimization in Partially Order Linear Spaces ” . Frankfurt : Lang .
   Google Scholar
• Jahn , J. 1988 . A generalization of a theorem of Arrow, Barankin and Blackwell . SIAM J. Control. Optim , 26 : 999 – 1005 .
   Web of Science ®Google Scholar
• Krein , M.G. and Rutman , M.A. 1950 . “ Linear operators leaving invariant a cone in a Banach space, AMS ” . Providence, RI Translation N 0 26
   Google Scholar
• Luc , D.T. 1989 . Theory of Vector Optimization , Springer-Verlag .
   Google Scholar
• Luc , D.T. 1990 . Contractibility of efficient points sets in normed spaces . Non linear Analysis , 15 : 527 – 535 .
   Web of Science ®Google Scholar
• Makarov E. K. Rachkowski N. N. Density theorems for generalized Henig proper efficiency J. Optim. Theory and Appl
   Google Scholar
• Naccache , P.H. 1978 . Connectedness of the set of nondominated outcomes in multicriteria optimization . J. Optim. Theory and Appl , 25 : 459 – 467 .
   Google Scholar
• Nieuwenhuis , J.W. 1982 . Some results about nondominated solutions . J. Optim. Theory Appl , 36 : 289 – 310 .
   Google Scholar
• Petshke , M. 1990 . On a theorem of Arrow-Barankin-Blackwell theorem . SIAIM J. Control Optim , 28 : 395 – 401 .
   Google Scholar
• Wen , Song. 1995 . A note on connectedness of efficient point sets . Arch. Math , 65 : 540 – 545 .
   Google Scholar
• Warburton , A.R. 1983 . Quasiconcave vector maximization: Connectedness of the sets of pareto-optimal and weak Pareto-optimal alternatives . J. Optim. Theory and Appl. , 40 : 537 – 557 .
   Web of Science ®Google Scholar
• Yu , P.L. 1974 . Cone convexity, cone extreme points and nondominated solutions in decision problems with multiobjectives . J. Optim. Theory and Appl , 14 : 319 – 377 .
   Web of Science ®Google Scholar
• Zhuang , D.M. 1994 . Density results for proper efficiencies . SIAM J. Control Optim , 32 : 51 – 58 .
   Web of Science ®Google Scholar