Rank-two programs involving linear fractional functions

Abstract

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 \(\phi \left( c^Tx+c_0,\frac{d^Tx+d_0}{b^Tx+b_0}\right) \) or \(\bar{\phi }\left( \frac{\bar{c}^Ty+\bar{c}_0}{a^Ty+a_0}, \frac{d^Ty+d_0}{b^Ty+b_0}\right) \). 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.