Efficiency and generalized convex duality for multiobjective programs. (English) Zbl 0686.90039

The author discusses duality relationships between the multiobjective nonlinear program Min f(x), subject to g(x)\(\geq 0\), and the two dual multiobjective programs, i.e. Wolfe’s vector dual and Mond-Weir’s vector dual. The results are obtained for convex functions, \(\rho\)-convex functions, and pseudoconvex functions. For the convex and \(\rho\)-convex functions a Wolfe type dual is formulated, while for the pseudoconvex and \(\rho\)-convex functions, a Mond-Weir type dual is proposed.
Reviewer: G.Chen


90C31 Sensitivity, stability, parametric optimization
49N15 Duality theory (optimization)
Full Text: DOI


[1] Chankong, V; Haimes, Y.Y, Multiobjective decision making: theory and methodology, (1983), North-Holland New York · Zbl 0525.90085
[2] Egudo, R.R, Proper efficiency and multiobjective duality in non-linear programming, J. inform. optim. sci., 8, 155-166, (1987) · Zbl 0642.90093
[3] Geoffrion, A.M, Proper efficiency and the theory of vector maximization, J. math. anal. appl., 22, 618-630, (1968) · Zbl 0181.22806
[4] Kuhn, H.W; Tucker, A.W, Nonlinear programming, (), 481-492 · Zbl 0044.05903
[5] Mangasarian, O.L, Nonlinear programming, (1969), McGraw-Hill New York · Zbl 0194.20201
[6] Mond, B; Weir, T, Generalized concavity and duality, (), 263-279 · Zbl 0538.90081
[7] Vial, J.P, Strong convexity of sets and functions, J. math. econom., 9, 187-205, (1982) · Zbl 0479.52005
[8] Vial, J.P, Strong and weak convexity of sets and functions, Math. oper. res., 8, 231-259, (1983) · Zbl 0526.90077
[9] {\scT. Weir}, Proper efficiency and duality for vector valued optimization problems, J. Austral. Math. Soc. Ser. A, in press. · Zbl 0616.90077
[10] Weir, T, A duality theorem for multiple objective fractional optimization problem, Bull. austral. math. soc., 34, 415-425, (1986) · Zbl 0596.90089
[11] Wolfe, P, A duality theorem for nonlinear programming, Quart. appl. math., 19, 239-244, (1961) · Zbl 0109.38406
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.