Duality in nonlinear fractional programming

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.The present research is partially supported by National Research Council of Canada.