On efficiency and duality for multiobjective programs. (English) Zbl 0764.90074

Summary: For a multiobjective nonlinear program which involved inequality and equality constraints, Wolfe, Mond-Weir, and general Mond-Weir type duals are formulated and the concept of efficiency (Pareto optimum) is used to state some duality results under generalized \((F,\rho)\)-convexity assumptions.


90C29 Multi-objective and goal programming
49N15 Duality theory (optimization)
90C26 Nonconvex programming, global optimization
26B25 Convexity of real functions of several variables, generalizations
Full Text: DOI


[1] Chankong, V.; Haimes, Y. Y., Multiobjective Decision Making: Theory and Methodology (1983), North-Holland: 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] Egudo, R. R., Efficiency and generalized convex duality for multiobjective programs, J. Math. Anal. Appl., 138, 84-94 (1989) · Zbl 0686.90039
[4] Geoffrion, A. M., Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl., 22, 618-630 (1968) · Zbl 0181.22806
[5] Hanson, M. A.; Mond, B., Further generalizations of convexity in mathematical programming, J. Inform. Optim. Sci., 3, 22-35 (1982) · Zbl 0475.90069
[6] Mond, B.; Weir, T., Generalized concavity and duality, (Schaible, S.; Ziemba, W. T., Generalized Concavity in Optimization and Economics (1981), Academic Press: Academic Press San Diego), 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] Weir, T., Proper efficiency and duality for vector valued optimization problems, J. Austral. Math. Soc. Ser. A (1989) · 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.