Well-Posedness for Tightly Proper Efficiency in Set-Valued Optimization Problem

ABSTRACT

In this paper, a characterization of tightly properly efficient solutions of set-valued optimization problem is obtained. The concept of the well-posedness for a special scalar problem is linked with the tightly properly efficient solutions of set-valued optimization problem.

In this paper, a characterization of tightly properly efficient solutions of set-valued optimization problem is obtained. The concept of the well-posedness for a special scalar problem is linked with the tightly properly efficient solutions of set-valued optimization problem.

Cite this paper

nullY. Xu and P. Zhang, "Well-Posedness for Tightly Proper Efficiency in Set-Valued Optimization Problem,"*Advances in Pure Mathematics*, Vol. 1 No. 4, 2011, pp. 184-186. doi: 10.4236/apm.2011.14032.

nullY. Xu and P. Zhang, "Well-Posedness for Tightly Proper Efficiency in Set-Valued Optimization Problem,"

References

[1] H. W. Kuhn and A. W. Tucker, “Nonlinear Programming,” Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, Berkele, 31 July-12 August 1950, pp. 481-492.

[2] A. M. Geoffrion, “Proper Efficiency and the Theory of Vector Maximization,” Journal of Mathematical Analysis and Applications, Vol. 22, No. 3, 1968, pp. 618-630.

[3] J. M. Borwein, “Proper Efficient Points for Maximizations with Respect to Cones,” SIAM Journal on Control and Optimization, Vol. 15, No. 1, 1977, pp. 57-63. doi:10.1137/0315004

[4] R. Hartley, “On Cone Efficiency, Cone convexity, and Cone Compactness,” SIAM Journal on Applied Mathematics, Vol. 34, No. 1, 1978, pp. 211-222. doi:10.1137/0134018

[5] H. P. Benson, “An Improved Definition of Proper Efficiency for Vector Maximization with Respect to Cones,” Journal of Mathematical Analysis and Applications, Vol. 71, No. 1, 1979, pp. 232-241. doi:10.1016/0022-247X(79)90226-9

[6] M. I. Henig, “Proper Efficiency with Respect to Cones,” Journal of Optimization Theory and Applications, Vol. 36, No. 3, 1982, pp. 387-407. doi:10.1007/BF00934353

[7] J. M. Browein and D. Zhuang, “Superefficiency in Vector Optimization,” Transactions of the American Mathematical Society, Vol. 338, No. 1, 1993, pp. 105-122. doi:10.2307/2154446

[8] A. Zaffaroni, “Degrees of Efficiency and Degrees of Minimality,” SIAM Journal on Control and Optimization, Vol. 42, No. 3, 2003, pp. 1071-1086. doi:10.1137/S0363012902411532

[9] J. Jahn, “Vector Optimization,” Springer-Verlag, Berlin, 2003.

[1] H. W. Kuhn and A. W. Tucker, “Nonlinear Programming,” Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, Berkele, 31 July-12 August 1950, pp. 481-492.

[2] A. M. Geoffrion, “Proper Efficiency and the Theory of Vector Maximization,” Journal of Mathematical Analysis and Applications, Vol. 22, No. 3, 1968, pp. 618-630.

[3] J. M. Borwein, “Proper Efficient Points for Maximizations with Respect to Cones,” SIAM Journal on Control and Optimization, Vol. 15, No. 1, 1977, pp. 57-63. doi:10.1137/0315004

[4] R. Hartley, “On Cone Efficiency, Cone convexity, and Cone Compactness,” SIAM Journal on Applied Mathematics, Vol. 34, No. 1, 1978, pp. 211-222. doi:10.1137/0134018

[5] H. P. Benson, “An Improved Definition of Proper Efficiency for Vector Maximization with Respect to Cones,” Journal of Mathematical Analysis and Applications, Vol. 71, No. 1, 1979, pp. 232-241. doi:10.1016/0022-247X(79)90226-9

[6] M. I. Henig, “Proper Efficiency with Respect to Cones,” Journal of Optimization Theory and Applications, Vol. 36, No. 3, 1982, pp. 387-407. doi:10.1007/BF00934353

[7] J. M. Browein and D. Zhuang, “Superefficiency in Vector Optimization,” Transactions of the American Mathematical Society, Vol. 338, No. 1, 1993, pp. 105-122. doi:10.2307/2154446

[8] A. Zaffaroni, “Degrees of Efficiency and Degrees of Minimality,” SIAM Journal on Control and Optimization, Vol. 42, No. 3, 2003, pp. 1071-1086. doi:10.1137/S0363012902411532

[9] J. Jahn, “Vector Optimization,” Springer-Verlag, Berlin, 2003.