# On the connectivity of efficient point sets

Applicationes Mathematicae (1998)

- Volume: 25, Issue: 1, page 121-127
- ISSN: 1233-7234

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topSong, Wen. "On the connectivity of efficient point sets." Applicationes Mathematicae 25.1 (1998): 121-127. <http://eudml.org/doc/219190>.

@article{Song1998,

abstract = {The connectivity of the efficient point set and of some proper efficient point sets in locally convex spaces is investigated.},

author = {Song, Wen},

journal = {Applicationes Mathematicae},

keywords = {vector optimization; efficient point sets; density; connectivity; efficient point set; locally convex spaces},

language = {eng},

number = {1},

pages = {121-127},

title = {On the connectivity of efficient point sets},

url = {http://eudml.org/doc/219190},

volume = {25},

year = {1998},

}

TY - JOUR

AU - Song, Wen

TI - On the connectivity of efficient point sets

JO - Applicationes Mathematicae

PY - 1998

VL - 25

IS - 1

SP - 121

EP - 127

AB - The connectivity of the efficient point set and of some proper efficient point sets in locally convex spaces is investigated.

LA - eng

KW - vector optimization; efficient point sets; density; connectivity; efficient point set; locally convex spaces

UR - http://eudml.org/doc/219190

ER -

## References

top- [1] J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley-Interscience, New York, 1984. Zbl0641.47066
- [2] H. P. Benson, An improved definition of proper efficiency for vector minimization with respect to cones, J. Math. Anal. Appl. 71 (1979), 232-241. Zbl0418.90081
- [3] G. R. Bitran and T. L. Magnanti, The structure of admissible points with respect to cone dominance, J. Optim. Theory Appl. 29 (1979), 573-614. Zbl0389.52021
- [4] J. M. Borwein, The geometry of Pareto efficiency over cones Math. Oper. Statist. Ser. Optim. 11 (1980), 235-248. Zbl0447.90077
- [5] J. M. Borwein and D. M. Zhuang, Super efficiency in vector optimization, Trans. Amer. Math. Soc. 338 (1993), 105-122. Zbl0796.90045
- [6] X. H. Gong, Connectedness of efficient solution sets for set-valued maps in normed spaces, J. Optim. Theory Appl. 83 (1994), 83-96. Zbl0845.90104
- [7] X. H. Gong, Connectedness of the efficient solution set of a convex vector optimization in normed spaces, Nonlinear Anal. 23 (1994), 1105-1114. Zbl0822.90115
- [8] X. H. Gong, Connectedness of super efficient solution sets for set-valued maps in Banach spaces, Math. Methods Oper. Res. 44 (1996), 135-145. Zbl0859.90109
- [9] A. Guerraggio, E. Molho and A. Zafferoni, On the notion of proper efficiency in vector optimization, J. Optim. Theory Appl. 82 (1994), 1-21. Zbl0827.90123
- [10] R. Hartley, On cone efficiency, cone convexity and cone compactness, SIAM J. Appl. Math. 34 (1978), 211-222. Zbl0379.90005
- [11] J.-B. Hiriart-Urruty, Images of connected sets by semicontinuous multifunctions, J. Math. Anal. Appl. 111 (1985), 407-422. Zbl0578.54013
- [12] Y. D. Hu and E. J. Sun, Connectedness of the efficient point set in strictly quasiconcave vector maximization, J. Optim. Theory Appl. 78 (1993), 613-622. Zbl0794.90051
- [13] J. Jahn, Mathematical Vector Optimization in Partially Ordered Linear Spaces, Lang, Frankfurt, 1986. Zbl0578.90048
- [14] B. L. Lin, P. K. Lin and S. L. Troyanski, Characterizations of denting points, Proc. Amer. Math. Soc. 102 (1988), 526-528. Zbl0649.46015
- [15] D. T. Luc, Theory of Vector Optimization, Springer, 1989.
- [16] D. T. Luc, Contractibility of efficient points sets in normed spaces, Nonlinear Anal. 15 (1990), 527-535. Zbl0718.90077
- [17] E. K. Makarov and N. N. Rachkovski, Density theorems for generalized Henig proper efficiency, J. Optim. Theory Appl. 91 (1996), 419-437. Zbl0871.90077
- [18] P. H. Naccache, Connectedness of the set of nondominated outcomes in multicriteria optimization, ibid. 25 (1978), 459-467. Zbl0363.90108
- [19] J. W. Nieuwenhuis, Some results about nondominated solutions, ibid. 36 (1982), 289-310. Zbl0452.90074
- [20] H. H. Schaefer, Topological Vector Spaces, Springer, New York, 1971.
- [21] W. Song, A note on connectivity of efficient point sets, Arch. Math. (Basel) 65 (1995), 540-545. Zbl0856.90096
- [22] W. Song, Connectivity of efficient solution sets in vector optimization of set-valued mappings, Optimization 39 (1997), 1-11. Zbl0867.90099
- [23] A. R. Warburton, Quasiconcave vector maximization: connectedness of the sets of Pareto-optimal and weak Pareto-optimal alternatives, J. Optim. Theory Appl. 40 (1983), 537-557. Zbl0496.90073
- [24] P. L. Yu, Cone convexity, cone extreme points and nondominated solutions in decision problems with multiobjectives, ibid. 14 (1974), 319-377. Zbl0268.90057

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