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Henig, Mordechai I.

Existence and characterization of efficient decisions with respect to cones. (English) Zbl 0477.90076

Math. Program. 23, 111-116 (1982).
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Cited in 20 Documents

MSC:

90C31 Sensitivity, stability, parametric optimization
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)

Keywords:

cones; existence; characterization theorems; efficient nondominated set of decisions; compactness conditions; multicriteria optimization; convex analysis
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\textit{M. I. Henig}, Math. Program. 23, 111--116 (1982; Zbl 0477.90076)
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References:

[1] K.J. Arrow, E.W. Barankin and D. Blackwell, ”Admissible points of convex sets”, in: H.W. Kuhn and A.W. Tucker, eds.,Contributions to the theory of games (Princeton University Press, Princeton, NJ, 1953) 87–91. · Zbl 0050.14203
[2] H.P. Benson, ”An improved definition of proper efficiency for vector maximization with respect to cones”,Journal of Mathematical Analysis and Applications 71 (1979) 232–241. · Zbl 0418.90081
[3] G.R. Bitran and T.L. Magnanti, ”The structure of admissible points with respect to cone dominance”,Journal of Optimization Theory and Applications 29 (1979) 573–614. · Zbl 0389.52021
[4] J.M. Borwein, ”The geometry of Pareto efficiency over cones”,Mathematische Operations-forschung und Statistik, Series Optimization 11 (1980) 235–248. · Zbl 0447.90077
[5] J.M. Borwein, ”Proper efficient points for maximization with respect to cones”,SIAM Journal on Control and Optimization 15 (1977) 57–63. · Zbl 0369.90096
[6] T.A. Brown and R.E. Strauch, ”Dynamic programming in multiplicative lattices”,Journal of Mathematical Analysis and Applications 12 (1965) 364–370. · Zbl 0132.40303
[7] R. Hartley, ”On cone-efficiency, cone-convexity, and cone compactness”,SIAM Journal on Applied Mathematics 34 (1978) 211–222. · Zbl 0379.90005
[8] H.W. Kuhn and A.W. Tucker, ”Nonlinear programming”, in: J. Neyman, ed.,Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, 1951). · Zbl 0044.05903
[9] R.T. Rockafellar, Convex analysis (Princeton University Press, Princeton, NJ, 1972). · Zbl 0224.49003
[10] P.L. Yu, ”Cone convexity, cone extreme-points, and nondominated solutions in decisions problems with multi-objectives”,Journal of Optimization Theory Applications 14 (1974) 319–377. · Zbl 0268.90057
[11] P.L. Yu and M. Zeleney, ”The set of all nondominated solutions in linear cases and a multicriteria simplex method”,Journal of Mathematical Analysis Applications 49 (1975) 430–468. · Zbl 0313.65047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.