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

##### MSC:
 90C31 Sensitivity, stability, parametric optimization 52A20 Convex sets in $n$ dimensions (including convex hypersurfaces)
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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 · doi:10.1016/0022-247X(79)90226-9 [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 · doi:10.1007/BF00934453 [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 · doi:10.1137/0315004 [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 · doi:10.1016/0022-247X(65)90045-4 [7] R. Hartley, ”On cone-efficiency, cone-convexity, and cone compactness”,SIAM Journal on Applied Mathematics 34 (1978) 211--222. · Zbl 0379.90005 · doi:10.1137/0134018 [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 · doi:10.1007/BF00932614 [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 · doi:10.1016/0022-247X(75)90189-4