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 φ ( cTx+c₀,dTx+d₀/bTx+b₀) ϕ c T x + c 0 , d T x + d 0 b T x + b 0 or φ ̄( c̄Ty+c̄₀aTy+a₀, dTy+d₀/bTy+b₀) 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.