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Dinh The Luc

On duality theory in multiobjective programming. (English) Zbl 0517.90076

J. Optimization Theory Appl. 43, 557-582 (1984).
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Cited in 1 Review
Cited in 25 Documents

MSC:

90C31 Sensitivity, stability, parametric optimization
90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
49N15 Duality theory (optimization)

Keywords:

vector-valued Lagrangian functions; duality theory; nonlinear multiobjective programming; saddle-point; vector-valued conjugate functions; M-convexity; Slater’s constraint qualification
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References:

[1] Tanino, T., andSawaragi, Y.,Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 27, pp. 509-529, 1979. · Zbl 0378.90100 · doi:10.1007/BF00933437
[2] Tanino, T., andSawaragi, Y.,Conjugate Maps and Duality in Multiobjective Optimization, Journal of Optimization Theory and Applications, Vol. 31, pp. 473-479, 1980. · Zbl 0418.90080 · doi:10.1007/BF00934473
[3] Bitran, G. R.,Duality for Nonlinear Multiple-Criteria Optimization Problems, Journal of Optimization Theory and Applications, Vol. 35, pp. 367-401, 1981. · Zbl 0445.90082 · doi:10.1007/BF00934908
[4] Corley, H. W.,Duality Theory for Maximizations with Respect to Cones, Journal of Mathematical Analysis and Applications, Vol. 84, pp. 560-568, 1981. · Zbl 0474.90081 · doi:10.1016/0022-247X(81)90188-8
[5] Rockafellar, T. R.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970. · Zbl 0193.18401
[6] Luenberger, D. G.,Optimization by Vector Space Methods, Wiley, New York, New York, 1969. · Zbl 0176.12701
[7] Luc, D. T.,M-Optimality and Dynamic Programming (to appear).
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