Nearly subconvexlike set-valued maps and vector optimization problems

Journal of Optimization Theory and Applications

Volumn 119, Issue 2, 2003, Pages 335-356

  Sach, P H ^a  

^a INSTITUTE OF MATHEMATICS   (Viet Nam)

Author keywords

Benson proper efficiency; Near cone subconvexlikeness; Saddle points; Vector optimization

Indexed keywords

SET THEORY;

BENSON PROPER EFFICIENCY; MAP OPTIMIZATIONS; NEAR CONE-SUBCONVEXLIKENESS; NEARLY SUBCONVEXLIKE; PROPER EFFICIENCY; SADDLE POINT; SET-VALUED MAP; VECTOR OPTIMIZATION PROBLEMS; VECTOR OPTIMIZATIONS; WEAKLY EFFICIENT SOLUTION;

MULTIOBJECTIVE OPTIMIZATION;

EID: 0345445976     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOTA.0000005449.20614.41     Document Type: Article

References (13)

1. YANG, X. M., LI, D., and WANG, S. Y., Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions, Journal of Optimization Theory and Applications, Vol. 110, pp. 413-427, 2001.
2. FAN, K., Minimax Theorems, Proceedings of the National Academy of Sciences of the USA, Vol. 39, pp. 42-47, 1953.
3. JEYAKUMAR, V., Convexlike Alternative Theorems and Mathematical Programming, Optimization, Vol. 16, pp. 643-652, 1985.
4. PAECK, S., Convexlike and Concavelike Conditions in Alternative, Minimax, and Minimization Theorems, Journal of Optimization Theory and Applications, Vol. 14, p. 317-332, 1992.
5. YANG, X. M., Alternative Theorems and Optimality Conditions with Weakened Convexity, Opsearch, Vol. 29. pp. 125-135, 1992.
6. CHEN, G. Y., and RONG, W. D., Characterization of the Benson Proper Efficiency for Nonconvex Vector Optimization, Journal of Optimization Theory and Applications, Vol. 98, pp. 365-384, 1998.
7. LI, Z. F., and WANG, S. Y., Lagrange Multipliers and Saddle Points in Multi-objective Programming, Journal of Optimization Theory and Applications, Vol. 83, pp. 63-81, 1994.
8. LI, Z. F., Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps, Journal of Optimization Theory and Applications, Vol. 98, pp. 623-649, 1998.
9. LI, Z., A Theorem of the Alternati√e and Its Applications to the Optimization of Set-Valued Maps, Journal of Optimization Theory and Applications, Vol. 100, pp. 365-375, 1999.
10. YANG, X. M., YANG, X. Q., and CHEN, G. Y., Theorems of the Alternative and Optimization with Set-Valued Maps, Journal of Optimization Theory and Applications, Vol. 107, pp. 627-640, 2000.
11. BRECKER, W. W., and KASSAY, G., A Systematization of Convexity Concepts for Sets and Functions, Journal of Convex Analysis, Vol. 4, pp. 109-127, 1997.
12. SONG, W., Duality in Set-Valued Optimization, Dissertations Mathematicae, Vol. 375, pp. 1-67, 1998.
13. DAUER, J. P., and SALEH, O. A., A Characterization of Proper Minimal Points as Solutions of Sublinear Optimization Problems, Journal of Mathematical Analysis and Applications, Vol. 178, pp. 227-246, 1993.