# Fast algorithms for convex-convex quadratic fractional programming

What are the fastest algorithm(s) (possibly approximation algorithms) for solving convex-convex quadratic fractional programming problems, i.e. optimization problems of the form

\begin{align*} \sup& &\frac{x^TQx}{x^TPx}\\ \text{s.t.}& &A^Tx \leq b\\ &&x\geq 0 \end{align*} where $$Q\in\mathbb{R}^{n\times n}$$ is a given symmetric positive semidefinite matrix, $$P\in\mathbb{R}^{n\times n}$$ is a given symmetric positive definite matrix, $$A \in \mathbb{R}^{m\times n}$$ is a given matrix, $$b \in\mathbb{R}^{m\times 1}$$ is a given column vector, and $$m,n \in \{1,2,...\}$$ are given.

I'm looking for algorithms that will run fast when $$m, n \leq 500$$.

Here's one algorithm that fits the bill:

R. Yamamoto and H. Konno: An efficient algorithm for solving convex-convex quadratic fractional programs. J. Optim. Theory Appl. 133 (2007), 241–255. DOI:10.1007/s10957- 007-9188-y

Are there any other algorithms that perform at least as fast as this one?