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Existence and characterization of efficient decisions with respect to cones. (English) Zbl 0477.90076
MSC:
90C31Sensitivity, stability, parametric optimization
52A20Convex sets in n dimensions (including convex hypersurfaces)
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.
[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.
[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).
[9]R.T. Rockafellar, Convex analysis (Princeton University Press, Princeton, NJ, 1972).
[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