Rank-two programs involving linear fractional functions

Abstract

AbstractThe 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 $$\phi \left( c^Tx+c_0,\frac{d^Tx+d_0}{b^Tx+b_0}\right) $$ ϕ c T x + c 0 , d T x + d 0 b T x + b 0 or $$\bar{\phi }\left( \frac{\bar{c}^Ty+\bar{c}_0}{a^Ty+a_0}, \frac{d^Ty+d_0}{b^Ty+b_0}\right) $$ ϕ ¯ c ¯ T y + c ¯ 0 a T y + a 0 , d T y + d 0 b T y + b 0 . 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.