Generalized \((F,\rho)\)-convexity and duality for nonsmooth multi- objective programs. (English) Zbl 0819.90082

Bhatia, D.; Jain, P.

Optimization 31, No. 2, 153-164 (1994).

Summary: \((F,\rho)\)-convexity and related definitions are extended for non-smooth functions, which are then used to establish duality results for multi- objective programs.

MSC:

90C29	Multi-objective and goal programming
26B25	Convexity of real functions of several variables, generalizations
49J52	Nonsmooth analysis

Keywords:

\((F,\rho)\)-convexity; non-smooth functions; duality results; multi- objective programs

References:

[1]	Bector C.R., Duality in Nonlinear fractional programming Zeitschrift für operations Research 17 pp 183– (1973) · Zbl 0267.90086
[2]	Bector C.R., On Duality with Generalized F-convexity Congressus Number-antium 80 pp 97– (1991)
[3]	Bhatia D., Non-Differentiable Multiobjectiv fractional Programming with Hanson Mond classes of functions Jr of Information and Optimization Sciences 12 (1) pp 35– (1991) · Zbl 0741.90074
[4]	Chankong V., Multiobjective Decision Making Theory and Methodology (1983) · Zbl 0622.90002
[5]	Clarke F.H., Optimization and non-Smoth Analysis (1983)
[6]	Egudo R.R., J Math Anal Appl 138 pp 84– (1989) · Zbl 0686.90039
[7]	Hanson M.A., Journal of Information and Optimization Sciencesl 4 pp 25– (1982) · Zbl 0475.90069
[8]	Mond, B. and Weir, T. 1981.Generalized convexity and duality in Generalized concavity in optimization and economics, Edited by: Schaible, S. and Ziemba, W.T. 263–279. San Diego: Academic Press. · Zbl 0538.90081
[9]	Preda V., JMAA 166 pp 365– (1992)
[10]	Schaible S., Operation Research 24 pp 452– (1976) · Zbl 0348.90120
[11]	Singh C., Jr of Inf and Opt Sciences 9 (2) pp 219– (1988)
[12]	Tanaka Y., Jr of Math Anal and Appl 144 (2) pp 342– (1989) · Zbl 0685.90089
[13]	Vial J.P., J Math Econom 9 (2) pp 187– (1982) · Zbl 0479.52005
[14]	Vial J.P., Math Oper Res 8 (2) pp 231– (1983) · Zbl 0526.90077
[15]	Wolfe P., Quari Appl Math 19 (2) pp 239– (1961)