Abstract
A vector-valued generalized Lagrangian is constructed for a nonlinear multiobjective programming problem. Using the Lagrangian, a multiobjective dual is considered. Without assuming differentiability, weak and strong duality theorems are established using Pareto efficiency.
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Egudo, R. R., andHanson, M. A.,Multiobjective Duality with Invexity, Journal of Mathematical Analysis and Applications, Vol. 126, pp. 469–477, 1987.
Iacob, P.,Saddle-Point Duality Theorems for Pareto Optimization, Analyse Numerique et Theorie de L'Approximation, Vol. 15, pp. 37–40, 1986.
Egudo, R. R.,Efficiency and Generalized Convex Duality for Multiobjective Programs, Journal of Mathematical Analysis and Applications Vol. 138, pp. 84–94, 1989.
Mond, B., Husain, I., andDurga Prasad, M. V.,Duality for a Class of Nondifferentiable Multiple-Objective Programming Problems, Journal of Information and Optimization Sciences, Vol. 9, pp. 331–341, 1988.
Preda, V.,On Efficiency and Duality for Multiobjective Programs, Journal of Mathematical Analysis and Applications, Vol. 166, pp. 365–377, 1992.
Bitran, G. R.,Duality for Nonlinear Multiple-Criteria Optimization Problems, Journal of Optimization Theory and Applications, Vol. 35, pp. 367–401, 1981.
Singh, C., andHanson, M. A.,Generalized Proper Efficiency in Multiobjective Programming, Journal of Information and Optimization Sciences, Vol. 12, pp. 139–144, 1991.
Singh, C., andHanson, M. A.,Erratum, Journal of Information and Optimization Sciences, Vol. 13, p. 173, 1992.
Weir, T., Mond, B., andCraven, B. D.,Weak Minimization and Duality, Numerical Functional Analysis and Optimization, Vol. 9, pp. 181–192, 1987.
Weir, T., andMond, B.,Preinvex Functions in Multiple-Objective Optimization, Journal of Mathematical Analysis and Applications, Vol. 136, pp. 29–38, 1988.
Rockafellar, R. T.,Lagrange Multipliers and Duality in Nonlinear Optimization, Quinta Escuela Latimo-Americana de Matematica, Mar del Plata, Argentina, 1980.
Bertsekas, D. P.,Constrained Optimization and Lagrange Multiplier Methods, Academic Press, London, England, 1982.
Dolecki, S., andKurcyusz, S.,On ϕ-Convexity in Extremal Problems, SIAM Journal on Control and Optimization, Vol. 16, pp. 277–300, 1978.
Gould, F. J.,Extensions of Lagrange Multipliers in Nonlinear Programming, SIAM Journal on Applied Mathematics, Vol. 17, pp. 1280–1297, 1969.
Gonen, A., andAvriel, M.,Duality in Nonlinear Programs Using Augmented Lagrangian Functions, Journal of Mathematical Analysis and Applications, Vol. 121, pp. 39–56, 1987.
Geoffrion, A. M.,Proper Efficiency and Theory of Vector Maximization, Journal of Mathematical Analysis and Applications, Vol. 22, pp. 618–630, 1968.
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Communicated by M. Avriel
The research of the second author was partially supported a GTE/SLU grant while visiting St. Lawrence University in the summer of 1991.
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Singh, C., Bhatia, D. & Rueda, N. Duality in nonlinear multiobjective programming using augmented Lagrangian functions. J Optim Theory Appl 88, 659–670 (1996). https://doi.org/10.1007/BF02192203
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DOI: https://doi.org/10.1007/BF02192203