Efficiency and duality for generalized convex multiobjective programming

• Autorzy: Yan, Z.-X.
• Języki publikacji: EN

Abstrakty

EN

Under a class of generalized (Type I, F, ρ)-convexity assumptions, the author formulates the sufficient conditions about Pareto efficiency and Geoffrion proper efficiency and gets the dual results between multiobjective programming and its Wolfe dual.

Słowa kluczowe

PL

(Type I, F, ρ)-funkcja wypukła

EN

(Type I, F, ρ)-convex function; Geoffrion proper efficiency; sublinear function

• Czasopismo: Journal of Applied Analysis
• Rocznik: 2008
• Tom: Vol. 14, nr 1
• Strony: 63-71
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Yan, Z.-X.

• University of Jinan. School of Science, Jinan, P. R. China,

Bibliografia

• [1] Chankong, V., Haimes, Y. Y., Multiobjective Decision Making Theory and Methodology, North-Holland, New York, 1983.
• [2] Geoffrion, A. M., Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl. 22 (1968), 613-630.
• [3] Hanson, M. A., Mond, B., Further generalizations of convexity in mathematical programming, J. Inform. Optim. Sci. 3 (1982), 22-35.
• [4] Hanson, M. A., Mond, B., Necessary and sufficient conditions in constrained optimization, Math. Programming 37 (1987), 51-58.
• [5] Kuhn. H. W., Tucker, A. W., Nonlinear programming, Proc. of the Second Berkeley Symposium on Mathematical Statistics and Probability (1950), Univ. Califormia Press, Berkeley-Los Angeles, 1951, 481-492.
• [6] Mangasarian, O. L., Nonlinear Programming, McGraw-Hill, New York, 1969.
• [7] Preda, V., On efficiency and duality for multiobjective programs, J. Math. Anal. Appl. 166 (1992), 365-377.
• [8] Wolfe, P., A duality theorem for nonlinear programming, Quart. Appl. Math. 19 (1961), 239-244.