Simplex-type algorithm for optimizing a pseudolinear quadratic fractional function over a polytope

Recently Cambini and Carosi described a characterization of pseudolinearity of quadratic fractional functions. A reformulation of their result was given by Rapcsák. Using this reformulation, in this paper we describe an alternative proof of the Cambini–Carosi Theorem. Our proof is shorter than the proof given by Cambini–Carosi and less involved than the proof given by Rapcsák. As an application we present a simplex-type algorithm for optimizing a pseudolinear quadratic fractional function over a polytope. Our algorithm works in a more general setting than the convex simplex algorithm adapted to the above problem.