Rank-two programs involving linear fractional functions

The aim of this paper is to deepen the study of solution methods for rank-two nonconvex problems with polyhedral feasible region, expressed by means of equality, inequality and box constraints, and objective function in the form of phi c T x + c 0 , d T x + d 0 b T x + b 0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi \left( c<^>Tx+c_0,\frac{d<^>Tx+d_0}{b<^>Tx+b_0}\right) $$\end{document} or phi over bar c over bar T y + c over bar 0 a T y + a 0 , d T y + d 0 b T y + b 0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{\phi }\left( \frac{\bar{c}<^>Ty+\bar{c}_0}{a<^>Ty+a_0}, \frac{d<^>Ty+d_0}{b<^>Ty+b_0}\right) $$\end{document} . These problems arise in bicriteria programs, quantitative management science, data envelopment analysis, efficiency analysis and performance measurement. Theoretical results are proved and applied to propose a solution algorithm. Computational results are provided, comparing various splitting criteria.