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

### 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 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.
##### Scheda breve Scheda completa Scheda completa (DC)
2024
Cambini, Riccardo; D’Inverno, Giovanna
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1232287
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