On efficient solutions in vector optimization

Journal of Optimization Theory and Applications

Volumn 96, Issue 1, 1998, Pages 201-209

  Deng, S ^a  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

efficient solutions; scalar optimization; Vector optimization; weakly efficient solutions

Indexed keywords

VECTORS;

EFFICIENT SOLUTION; LINEAR VECTORS; OPTIMIZATION PROBLEMS; SCALAR OPTIMIZATION; VECTOR OPTIMIZATION PROBLEMS; VECTOR OPTIMIZATIONS; WEAKLY EFFICIENT SOLUTION;

MULTIOBJECTIVE OPTIMIZATION;

EID: 10344247737     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022627520279     Document Type: Article

References (10)

1. BORWEIN, J. M., On the Existence of Pareto Efficient Points, Mathematics of Operations Research, Vol. 8, pp. 64-73, 1983.
2. SAWARAGI, Y., NAKAYAMA, H., and TANINO, T., Theory of Multiobjective Optimization, Academic Press, New York, New York, 1985.
3. HENIG, M. I., Existence and Characterization of Efficient Decisions with Respect to Cones, Mathematical Programming, Vol. 23, pp. 111-116, 1982.
4. BITRAN, G. R., and MAGNANTI, T. L., The Structure of Admissible Points with Respect to Cone Dominance, Journal of Optimization Theory and Applications, Vol. 29, pp. 573-614, 1979.
5. RUIZ-CANALES, P., and RUFIAN-LIZANA, A., A Characterization of Weakly Efficient Points, Mathematical Programming, Vol. 68, pp. 205-212, 1995.
6. ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
7. HIRIART-URRUTY, J. B., and LEMARECHAL, C., Convex Analysis and Minimization Algorithms, Vol. 1, Springer Verlag, Berlin, Germany, 1993.
8. DENG, S., Characterizations of the Nonemptiness and Compactness of Solution Sets in Convex Vector Optimization, Journal of Optimization Theory and Applications, Vol. 96, pp. 123-131, 1998.
9. CHENG, G. Y. and CRAVEN, B. D., Existence and Continuity of Solutions for Vector Optimization, Journal of Optimization Theory and Applications, Vol. 81, pp. 459-467, 1994.
10. DENG, S., On Approximate Solutions in Convex Vector Optimization, SIAM Journal on Control and Optimization, Vol. 35, pp. 2128-2136, 1997.