Properly Maximal Points in Product Spaces

Published Online:https://doi.org/10.1287/moor.1050.0180

References

  • Arrow K., Barankin E., Blackwell D., Kuhn H. W., Tucker A. W. Admissible points of convex sets. Contributions to the Theory of Games (1953) (Princeton University Press, Princeton, NJ) 87–92Google Scholar
  • Benson H. P. An improved definition of proper efficiency for vector minimization with respect to cones. J. Math. Anal. Appl. (1978) 71:232–241CrossrefGoogle Scholar
  • Borwein J. M., Zhuang D. Super efficiency in convex vector optimization. Trans. Amer. Math. Soc. (1993) 338:105–122CrossrefGoogle Scholar
  • Cheng Y. H., Fu W. T. Strong efficiency in a locally convex space. Math. Methods Oper. Res. (1999) 50:373–384CrossrefGoogle Scholar
  • Daniilidis A. Arrow-Barankin-Blackwell theorems and related results in cone duality: A survey. Lecture Notes in Economics and Mathematical Systems (2000) 481(Springer, Berlin, Germany) 119–131Google Scholar
  • Geoffrion A. M. Proper efficiency and related cone results in vector optimization theory. J. Math. Anal. Appl. (1968) 22:618–630CrossrefGoogle Scholar
  • Guerraggio A., Molho E., Zaffaroni A. On the notion of proper efficiency in vector optimization. J. Optim. Theory Appl. (1994) 82:1–21CrossrefGoogle Scholar
  • Ha T. X. D. Existence and density results for proper efficiency in cone compact sets. Optimization (2001) 111:173–194Google Scholar
  • Hartley R. On cone efficiency, cone convexity, and cone compactness. SIAM J. Appl. Math. (1978) 34:211–222CrossrefGoogle Scholar
  • Henig M. I. Proper efficiency with respect to cones. J. Optim. Theory Appl. (1982) 36:387–407CrossrefGoogle Scholar
  • Jahn J. A generalization of a theorem of Arrow, Barankin and Blackwell. SIAM J. Control Optim. (1988) 26:999–1005CrossrefGoogle Scholar
  • Kuhn H. W., Tucker A. W. Nonlinear programming. Proc. 2nd Berkeley Sympos. Math. Statist. Probab. (1951) Berkeley, CA:481–492Google Scholar
  • Makarov E. K., Rachkovski N. N. Density theorems for generalized Henig proper efficiency. J. Optim. Theory Appl. (1996) 91:419–437CrossrefGoogle Scholar
  • Luc D. T.Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems (1989) 319(Springer, Berlin, Germany) Google Scholar
  • Luc D. T. On the properly efficient points of nonconvex sets. Eur. J. Oper. Res. (1995) 86:332–336CrossrefGoogle Scholar
  • Luc D. T. Recessively compact sets: Properties and uses. Set-Valued Anal. (2002) 10:15–35CrossrefGoogle Scholar
  • Luc D. T., Penot J. P. Convergence of asymptotic directions. Trans. Amer. Math. Soc. (2001) 353:4095–4121CrossrefGoogle Scholar
  • Yang X. M., Li D., Wang S. Y. Nearly-subconvexlikeness in vector optimization with set-valued functions. J. Optim. Theory Appl. (2001) 110:413–427CrossrefGoogle Scholar
  • Zheng X. Y. Proper efficiency in locally convex topological vector spaces. J. Optim. Theory Appl. (1997) 94:469–486CrossrefGoogle Scholar
  • Zhuang D. Density results for proper efficiencies. SIAM J. Control Optim. (1994) 32:51–58CrossrefGoogle Scholar
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