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Some results on mathematical programming with generalized ratio invexity. (English) Zbl 0946.90089

Summary: A generalized ratio invexity concept has been applied for single objective fractional programming problems. A concept which has been invoked seems to be more general than the one used earlier by Khan and Hanson in such contexts. Further, duality results for fractional programs have also been obtained.

MSC:

90C32 Fractional programming
90C46 Optimality conditions and duality in mathematical programming
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[1] Israel, A.Ben; Mond, B., What is invexity?, J. austral. math. soc. ser. B, 28, 1-9, (1985) · Zbl 0603.90119
[2] Craven, B.D., Invex functions and constrained local minima, Bull. austral. math. soc., 24, 357-366, (1981) · Zbl 0452.90066
[3] Craven, B.D., Duality for the generalized convex fractional programs, (), 473-490 · Zbl 0534.90089
[4] Craven, B.D.; Glover, B.M., Invex functions and duality, J. austral. math. soc. ser. A, 39, 1-20, (1985) · Zbl 0565.90064
[5] Egudo, R.R.; Hanson, M.A., Multiobjective duality with invexity, J. math. anal. appl., 126, 469-477, (1987) · Zbl 0635.90086
[6] Hanson, M.A., A duality theorem in nonlinear programming with nonlinear constraints, Austral. J. statist., 3, 67-71, (1961)
[7] Hanson, M.A., On sufficiency of the kuhn – tucker conditions, J. math. anal. appl., 80, 544-550, (1981) · Zbl 0463.90080
[8] Jeyakumar, V., Strong and weak invexity in mathematical programming, Math. oper. res., 55, 109-125, (1985) · Zbl 0566.90086
[9] Jeyakumar, V.; Mond, B., On generalized convex mathematical programming, J. austral. math. soc. ser. B, 34, 43-53, (1992) · Zbl 0773.90061
[10] Khan, Z.A., Sufficiency and duality theory for a class of differentiable multiobjective programming problems with invexity, ()
[11] Khan, Z.A.; Hanson, M.A., On ratio invexity in mathematical programming, J. math. anal. appl., 205, 330-336, (1997) · Zbl 0872.90094
[12] Mangasarian, O.L., Nonlinear programming, (1969), McGraw Hill New York · Zbl 0194.20201
[13] Reiland, T.W., Nonsmooth invexity, Bull. austral. math. soc., 42, 437-446, (1990) · Zbl 0711.90072
[14] Singh, C.; Hanson, M.A., Multiobjective fractional programming duality theory, Naval res. logist., 38, 925-933, (1991) · Zbl 0749.90068
[15] Suneja, S.K.; Lalitha, C.S., Multiobjective fractional programming involving ρ-invex and related function, Opsearch, 30, 1-14, (1993) · Zbl 0793.90081
[16] T. Weir, A note on invex functions and duality in generalized fractional programming, Research Report, Department of Mathematics, The University of New South Wales, ACT 2600, Australia, 1990.
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