Rank-two programs involving linear fractional functions

Riccardo Cambini () and Giovanna D’Inverno ()
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Riccardo Cambini: University of Pisa
Giovanna D’Inverno: University of Pisa

Decisions in Economics and Finance, 2024, vol. 47, issue 1, No 12, 299-325

Abstract: 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 $$\phi \left( c^Tx+c_0,\frac{d^Tx+d_0}{b^Tx+b_0}\right) $$ 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.

Keywords: Nonlinear programming; Low-rank structures; Linear fractional programs; Optimal level solutions; Global optimization; 90C30; 90C26; 90C32; 90C30; 90C26; 90C32 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10203-024-00444-2

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