A note on duality in homogeneous fractional programming

For a linear fractional programming problem, Sharma and Swarup have constructed a dual problem, also a linear fractional program, in which the objective functions of both primal and dual problems are the same. Craven and Mond have extended this result to a nonlinear fractional programming problem with linear constraints, and a dual problem for which the objective function is the same as that of the primal. This theorem is now further extended from linear to differentiable convex constraints.     

On fractional programming and equivalence

Under fairly general conditions, a nonlinear fractional program, where the function to be maximized has the form f(x)/g(x), is shown to be equivalent to a nonlinear program not involving fractions. The latter program is not generally a convex program, but there is often a convex program equivalent to it, to which the known algorithms for convex programming may be applied. An application to duality of a fractional program is discussed.     

On a constraint qualification in a nondifferentiable programming problem

A mathematical programming problem with an objective function containing the square root of a positive semidefinite quadratic form has been considered by Mond. In order to use a transposition theorem of Eisenberg, Mond introduces a complicated constraint qualification. In this note we give a simple geometric characterization to this constraint qualification and show that it is implied by the generalized Slater constraint qualification.