Summary
The purpose of the present paper is to introduce, on the lines similar to that ofWolfe [1961], a dual program to a nonlinear fractional program in which the objective function, being the ratio of a convex function to a strictly positive linear function, is a special type of pseudo-convex function and the constraint set is a convex set constrained by convex functions in the form of inequalities. The main results proved are, (i) Weak duality theorem, (ii)Wolfe's (Direct) duality theorem and (iii)Mangasarian's Strict Converse duality theorem.Huard's [1963] andHanson's [1961] converse duality theorems for the present problem have just been stated because they can be obtained as a special case ofMangasarian's theorem [1969, p. 157]. The other important discussion included is to show that the dual program introduced in the present paper can also be obtained throughDinkelbach's Parametric Replacement [1967] of a nonlinear fractional program. Lastly, duality in convex programming is shown to be a special case of the present problem.
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The present research is partially supported by National Research Council of Canada.
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Bector, C.R. Duality in nonlinear fractional programming. Zeitschrift für Operations Research 17, 183–193 (1973). https://doi.org/10.1007/BF01951417
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DOI: https://doi.org/10.1007/BF01951417