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Efficient and weak efficient points in vector optimization with generalized cone convexity. (English) Zbl 1055.90062

Summary: We present necessary and sufficient conditions of efficiency and weak efficiency under generalized cone-convexity and cone-subconvexity. The results are stated in partially ordered real linear spaces from a separation theorem between convex cones which need not be solid.

MSC:

90C29 Multi-objective and goal programming
90C48 Programming in abstract spaces
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[1] Yu, P. L., Cone convexity, cone extreme points, and nondominated solutions in decision problems with multi-objectives, Journal of Optimization Theory and Applications, 14, 3, 319-377 (1974) · Zbl 0268.90057
[2] Fan, K., Minimax theorems, (Proceedings of the National Academy of Sciences of the USA, 39 (1953)), 42-47 · Zbl 0050.06501
[3] Jeyakumar, V., A generalization of a minimax theorem of Fan via a theorem of the alternative, Journal of Optimization Theory and Applications, 48, 525-533 (1986) · Zbl 0563.49006
[4] Yang, X., Alternative theorems and optimality conditions with weakened convexity, Opsearch, 29, 125-135 (1992) · Zbl 0757.90075
[5] Adán, M.; Novo, V., Optimality conditions for vector optimization problems with generalized convexity in real linear spaces, Optimization, 51, 1, 73-91 (2002) · Zbl 1012.90054
[6] Holmes, R. B., Geometric Functional Analysis and its Applications (1975), Springer-Verlag: Springer-Verlag New York · Zbl 0336.46001
[7] Jahn, J., Mathematical Vector Optimization in Partially Ordered Linear Spaces (1986), Verlag Peter Lang: Verlag Peter Lang Frankfurt · Zbl 0578.90048
[8] Li, Z. F.; Wang, S. X., Lagrange multipliers and saddle points in multiobjective programming, Journal of Optimization Theory and Applications, 83, 63-81 (1994) · Zbl 0823.90107
[9] Yang, X., Generalized subconvexlike functions and multiple objective optimization, Systems Science and Mathematical Sciences, 8, 3, 254-259 (1995) · Zbl 0840.90115
[10] Breckner, W. W.; Kassay, G., A systematization of convexity concepts for sets and functions, Journal of Convex Analysis, 4, 109-127 (1997) · Zbl 0885.52003
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