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Quasiconcave vector maximization: Connectedness of the sets of Pareto- optimal and weak Pareto-optimal alternatives. (English) Zbl 0496.90073

90C31Sensitivity, stability, parametric optimization
Full Text: DOI
[1] Naccache, P. H.,Connectedness of the Set of Nondominated Outcomes in Multicriteria Optimization, Journal of Optimization Theory and Applications, Vol. 25, pp. 459-467, 1978. · Zbl 0363.90108 · doi:10.1007/BF00932907
[2] Bitran, G. R., andMagnanti, T. L.,The Structure of Admissible Points with respect to Cone Dominance, Journal of Optimization Theory and Applications, Vol. 29, pp. 573-614, 1979. · Zbl 0389.52021 · doi:10.1007/BF00934453
[3] Yu, P. L., andZeleny, M.,The Set of All Nondominated Solutions in Linear Cases and the Multicriteria Simplex Method, Journal of Optimization Theory and Applications, Vol. 19, pp. 430-460, 1975. · Zbl 0313.65047
[4] Choo, E. U., andAtkins, D. R.,Connectedness in Multiple Criteria Linear Fractional Programming, Management Science (to appear).
[5] Schaible, S.,Fractional Programming: Applications and Algorithms, European Journal of Operational Research, Vol. 7, pp. 111-120, 1981. · Zbl 0452.90079 · doi:10.1016/0377-2217(81)90272-1
[6] Ashton, D., andAtkins, D.,Multicriteria Programming for Financial Planning, Journal of the Operational Research Society, Vol. 3, pp. 259-270, 1979. · Zbl 0393.90048
[7] Kornbluth, J., andSteuer, R.,Multiple-Objective Linear Fractional Programming, Management Science, Vol. 27, pp. 1024-1039, 1981. · Zbl 0467.90064 · doi:10.1287/mnsc.27.9.1024
[8] Geoffrion, A. M., Dyer, J. S., andFeinberg, A.,An Interactive Approach for Multi-Criterion Optimization with an Application to the Operation of an Academic Department, Management Science, Vol. 19, pp. 357-368, 1972. · Zbl 0247.90069 · doi:10.1287/mnsc.19.4.357
[9] Warburton, A. R.,Topics in Multiple Criteria Optimization, University of British Columbia, Vancouver, Canada, Faculty of Commerce and Business Administration, PhD Thesis, 1981.
[10] Hildenbrand, W., andKirman, A. P.,Introduction to Equilibrium Analysis, American Elsevier Publishing Company, New York, New York, 1976. · Zbl 0345.90004
[11] Bowman, V. J.,On the Relationship of the Tchebycheff Norm and the Efficient Frontier of Multiple-Criteria Objectives, Multiple Criteria Decision Making, Edited by S. Zionts and H. Thiriez, Springer-Verlag, Berlin, 1975.
[12] Avriel, M.,Generalized Concavity, Proceedings of the NATO Advanced Study Institute on Generalized Concavity in Optimization and Economics, University of British Columbia, Vancouver, Canada, 1980 (to appear).
[13] Zang, I.,Concavifiability of C 2 Functions: A Unified Approach, Proceedings of the NATO Advanced Study Institute on Generalized Concavity in Optimization and Economics, University of British Columbia, Vancouver, Canada, 1980 (to appear).