×

zbMATH — the first resource for mathematics

Efficiency in multiple objective optimization problems. (English) Zbl 0362.90092

MSC:
90C30 Nonlinear programming
90C05 Linear programming
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] H.P. Benson and T.L. Morin, ”The vector maximization problem: proper efficiency and stability”,SIAM Journal on Applied Mathematics, to appear. · Zbl 0357.90059
[2] A. Charnes and W.W. Cooper,Management models and industrial applications of linear programming, vol. 1 (Wiley, New York, 1961). · Zbl 0107.37004
[3] J.G. Ecker and I.A. Kouada, ”Finding efficient points for linear multiple objective programs”,Mathematical Programming 3 (1975) 375–377. · Zbl 0385.90105 · doi:10.1007/BF01580453
[4] J.P. Evans and R.E. Steuer, ”A revised simplex method for linear multiple objective programs”,Mathematical Programming 4 (1972) 54–72. · Zbl 0281.90045
[5] A.M. Geoffrion, ”Proper efficiency and the theory of vector maximization”,Journal of Mathematical Analysis and Applications 22 (3) (1968) 618–630. · Zbl 0181.22806 · doi:10.1016/0022-247X(68)90201-1
[6] A.M. Geoffrion, ”Duality in nonlinear programming”,SIAM Review 13 (1971) 1–37. · Zbl 0232.90049 · doi:10.1137/1013001
[7] H. Isermann, ”Proper efficiency and the linear vector maximum problem”,Operations Research 22 (1) (1974) 189–191. · Zbl 0274.90024 · doi:10.1287/opre.22.1.189
[8] T. Koopmans, ”Analysis of production as an efficient combination of activities”, in:activity analysis of production and allocation, Cowles Commission Monograph vol. 13 (Wiley, New York, 1951) pp. 33–97. · Zbl 0045.09506
[9] E.L. Peterson and J.G. Ecker, ”A unified duality theory for quadratically constrained quadratic programs andl p -constrainedl p -approximation problems”,Bulletin of the American Mathematical Society 74 (1968) 316–321. · Zbl 0155.28502 · doi:10.1090/S0002-9904-1968-11938-X
[10] E.L. Peterson and J.G. Ecker, ”Geometric programming: duality in quadratic programming andl p -approximation I”, in: H.W. Kuhn and A.W. Tucker, eds.,Proceedings of international symposium on mathematical programming (Princeton, NJ 1967).
[11] E.L. Peterson and J.G. Ecker, ”Geometric programming: duality in quadratic programming andl p -approximation II (canonical programs)”,SIAM Journal on Applied Mathematics 17 (1969) 317–340. · Zbl 0172.43704 · doi:10.1137/0117031
[12] E.L. Peterson and J.G. Ecker, ”Geometric programming: duality in quadratic programming andl p -approximation III (degenerate programs)”,Journal of Mathematical Analysis and Applications 29 (1970) 365–383. · Zbl 0183.49003 · doi:10.1016/0022-247X(70)90085-5
[13] J. Philip, ”Algorithms for the vector maximization problem”,Mathematical Programming 2 (1972) 207–229. · Zbl 0288.90052 · doi:10.1007/BF01584543
[14] R.T. Rockafellar, ”Lagrange multipliers in optimization”, in: R.W. Cottle, ed.,Proceedings of symposia in applied mathematics IX, (Am. Math. Soc., Providence, RI, to appear). · Zbl 0341.90046
[15] R.T. Rockafellar, ”Ordinary convex programs without a duality gap”,Journal of Optimization Theory and Applications 7 (3) (1971) 143–148. · Zbl 0198.24604 · doi:10.1007/BF00932472
[16] R.T. Rockafellar, ”Some convex programs whose duals are linearly constrained”, in:Nonlinear programming (Academic Press, New York, 1970) pp. 293–322. · Zbl 0252.90046
[17] R.E. Wendell, A.P. Hurter, Jr. and T.J. Lowe, ”Efficient points in location problems”,Journal of Mathematical Analysis and Applications 49 (2) (1975) 430–468. · Zbl 0313.65047 · doi:10.1016/0022-247X(75)90189-4
[18] P.L. Yu and M. Zeleny, ”The set of all nondominated solutions in linear cases and a multicriteria simplex method”,AIIE Transactions, to appear. · Zbl 0313.65047
[19] P.L. Yu and M. Zeleny, ”On some linear multi-parametric programs”, Rept. No. CSS 73-05, Center for System Science, University of Rochester, Rochester, NY (1973).
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.