Taiwanese Journal of Mathematics

AN EVALUATION OF EFFICIENT POINTS FOR VECTOR OPTIMIZATION

Tetsuya Nuriya and Daishi Kuroiwa

Full-text: Open access

Abstract

In this paper, to decide the best point of many efficient points in vector optimization, we consider an evaluate method of efficient points for solutions in vector optimization problem. We introduce an evaluate function of efficient points, and show properties of the evaluate function.

Article information

Source
Taiwanese J. Math., Volume 12, Number 8 (2008), 2063-2082.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405136

Digital Object Identifier
doi:10.11650/twjm/1500405136

Mathematical Reviews number (MathSciNet)
MR2459814

Zentralblatt MATH identifier
1194.90090

Subjects
Primary: 90C29: Multi-objective and goal programming
Secondary: 46A40: Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]

Keywords
vector optimization efficiency proper efficiency weakly efficiency ideal efficiency unified representation

Citation

Nuriya, Tetsuya; Kuroiwa, Daishi. AN EVALUATION OF EFFICIENT POINTS FOR VECTOR OPTIMIZATION. Taiwanese J. Math. 12 (2008), no. 8, 2063--2082. doi:10.11650/twjm/1500405136. https://projecteuclid.org/euclid.twjm/1500405136


Export citation

References

  • Harold P. Benson, An improved Definition of proper efficiency for vector maximization with respect to cones, Journal of Mathematical Analysis and Applications, 71 (1979), 232-241.
  • J.Borwein, Proper efficient points for maximizations with respect to cones, SIAM Journal on Control and Optimization, 15 (1977), 57-63.
  • J. M. Borwein, D. Zhuang, Super efficiency in vector optimization, Transactions of The American Mathematical Society, 338 (1993) 1, 105-122.
  • M. I.Henig, Proper efficiency with respect to cones, Journal of Optimization Theory and Applications, 36 (1982), 387-407.
  • S. Helbig, Approximation of the efficient point set by perturbation of the ordering cone, Methods and Models of Operations Research, 35 (1991), 197-220.
  • J. W. Nieuwenhuis, Properly efficient and efficient solutions for vector maximization problems in Euclidean space, Journal of Mathematical Analysis and Applications, 84 (1981), 311-317.
  • D. Zhuang, Density results for proper efficiencies, SIAM Journal on Control and Optimization, 32 (1994), 51-58.
  • X. Y. Zheng, Scalarization of Henig proper efficient points in a normed space, Journal of Optimization Theory and Applications, 105(1) (1994), 233-247.
  • D. T. Luc, Theory of vector optimization, Lecture Notes in Economics and Mathematical Systems, 319, Springer-Verlag, Berlin, 1989.