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.
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.
