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Rank-two programs involving linear fractional functions

Author

Listed:
  • Riccardo Cambini

    (University of Pisa)

  • Giovanna D’Inverno

    (University of Pisa)

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.

Suggested Citation

  • Riccardo Cambini & Giovanna D’Inverno, 2024. "Rank-two programs involving linear fractional functions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 299-325, June.
    • Handle: RePEc:spr:decfin:v:47:y:2024:i:1:d:10.1007_s10203-024-00444-2
    DOI: 10.1007/s10203-024-00444-2
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    References listed on IDEAS

    as
    1. Riccardo Cambini, 2020. "Underestimation functions for a rank-two partitioning method," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 465-489, December.
    2. Riccardo Cambini & Laura Carosi & Laura Martein & Ezat Valipour, 2017. "Simplex-like sequential methods for a class of generalized fractional programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 77-96, February.
    3. Riccardo Cambini & Claudio Sodini, 2010. "Global optimization of a rank-two nonconvex program," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 165-180, February.
    4. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    5. Riccardo Cambini & Laura Carosi & Laura Martein, 2017. "Generating the efficient frontier of a class of bicriteria generalized fractional programming," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 81-101, November.
    6. Riccardo Cambini & Claudio Sodini, 2008. "A sequential method for a class of box constrained quadratic programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 223-243, April.
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