Complex fractional programming and the Charnes–Cooper transformation

We extend the Charnes–Cooper transformation to complex fractional programs involving continuous complex functions and analytic functions. Such problems are shown to be equivalent to nonfractional complex programming problems. This technique is employed also to reduce complex linear fractional programs to complex linear programs. More generally, it can be shown that the convex–concave fractional programming problems are equivalent to complex convex nonfractional programs using the generalized Charnes–Cooper transformation.