×

zbMATH — the first resource for mathematics

Efficiency and proper efficiency in vector maximization with respect to cones. (English) Zbl 0519.90080

MSC:
90C31 Sensitivity, stability, parametric optimization
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Benson, H.P, Existence of efficient solutions for vector maximization problems, J. optim. theory appl., 26, 569-580, (1978) · Zbl 0373.90085
[2] Benson, H.P, An improved definition of proper efficiency for vector maximization with respect to cones, J. math. anal. appl., 71, 232-241, (1979) · Zbl 0418.90081
[3] Benson, H.P; Morin, T.L, The vector maximization problem: proper efficiency and stability, SIAM J. appl. math., 32, 64-72, (1977) · Zbl 0357.90059
[4] Borwein, J, Proper efficient points for maximizations with respect to cones, SIAM J. control optim., 15, 57-63, (1977) · Zbl 0369.90096
[5] Canon, M.D; Cullum, C.D; Polak, E, Theory of optimal control and mathematical programming, () · Zbl 0186.24002
[6] Charnes, A; Cooper, W.W, ()
[7] Ecker, J.G; Kouada, I.A, Finding efficient points for linear multiple objective programs, Math. programming, 8, 375-377, (1975) · Zbl 0385.90105
[8] Geoffrion, A.M, Proper efficiency and the theory of vector maximization, J. math. anal. appl., 22, 618-630, (1968) · Zbl 0181.22806
[9] Kelley, J.L; Namioka, I, Linear topological spaces, (1963), Van Nostrand Princeton, N.J
[10] Kuhn, H.W; Tucker, A.W, Nonlinear programming, (), 481-492 · Zbl 0044.05903
[11] Luenberger, D.G, Optimization by vector space methods, (1969), Wiley New York · Zbl 0176.12701
[12] Peterson, E.L, Symmetric duality for generalized unconstrained geometric programming, SIAM J. appl. math., 19, 487-526, (1970) · Zbl 0205.48001
[13] Rockafellar, R.T, Duality and stability in extremum problems involving convex functions, Pacific J. math., 21, 167-187, (1967) · Zbl 0154.44902
[14] Rockafellar, R.T, Duality in nonlinear programming, (), 401-422 · Zbl 0231.90037
[15] Rockafellar, R.T, Convex analysis, (1970), Princeton Univ. Press Princeton, N.J · Zbl 0202.14303
[16] Varaiya, P.P, Nonlinear programming in Banach space, SIAM J. appl. math., 15, 284-293, (1967) · Zbl 0171.18004
[17] Wendell, R.E; Lee, D.N, Efficiency in multiple objective optimization problems, Math. programming, 12, 406-414, (1977) · Zbl 0362.90092
[18] Wijsman, R.A, Convergence of sequences of convex sets, cones and functions, Bull. amer. math. soc., 70, 186-188, (1964) · Zbl 0121.39001
[19] Yu, P.L, Cone convexity cone extreme points, and nondominated solutions in decision problems with multiobjectives, J. optim. theory appl., 14, 319-377, (1974) · Zbl 0268.90057
[20] Zeleny, M, Linear multiobjective programming, (1974), Springer-Verlag New York · Zbl 0325.90033
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.