Skip to main content
SpringerLink
Log in

Generation of disjointly constrained bilinear programming test problems

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

This paper describes a technique for generating disjointly constrained bilinear programming test problems with known solutions and properties. The proposed construction technique applies a simple random transformation of variables to a separable bilinear programming problem that is constructed by combining disjoint low-dimensional bilinear programs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Gallo and A. Ülkücü, “Bilinear programming: an exact algorithm,” Math. Programming, vol. 12, pp. 173–194, 1977.

    Google Scholar 

  2. J. Judice and A. Faustino, “A computational analysis of LCP methods for bilinear and concave quadratic programming,” Comput. Oper. Res., vol. 18, pp. 645–654, 1991.

    Google Scholar 

  3. H. Konno, “Bilinear programming — Part II — Applications,” Dept. of Oper. Res. Tech. Report No. 71-10, Stanford Univ., 1971.

  4. H. Konno, “A cutting plane algorithm for solving bilinear programs,” Math. Programming, vol. 11, pp. 14–27, 1976.

    Google Scholar 

  5. H. Konno, “Maximization of a convex quadratic function under linear constraints,” Math. Programming, vol. 11, pp. 117–127, 1976.

    Google Scholar 

  6. S. Sahni, “Computational related topics,” SIAM J. Comput., vol. 3, pp. 262–279, 1974.

    Google Scholar 

  7. H. Sherali and C. Shetty, “A finitely convergent algorithm for bilinear programming problems using polar cuts and disjunctive face cuts” Math. Programming, vol. 19, pp. 14–31, 1980.

    Google Scholar 

  8. H. Vaish, “Nonconvex programming, with applications to production and location problem,” PhD thesis, Georgia Inst. of Tech., 1974 (unpublished).

  9. H. Vaish and C. Shetty, “The bilinear programming problem,” Nav. Res. Logistics Q., vol. 23, pp. 303–309, 1976.

    Google Scholar 

  10. H. Vaish and C. Shetty, “A cutting plane algorithm for bilinear programming problem,” Nav. Res. Logistics Q., vol. 24, 83–94, 1977.

    Google Scholar 

  11. Y. Yajima and H. Konno, “Efficient algorithms for solving rank two and rank three bilinear programming problems,” J. of Global Optimization, vol. 1, pp. 155–171, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departmento de Matemática, Universidade de Coimbra, 3000, Coimbra, Portugal

    Luis N. Vicente

  2. Department of Systems Design Engineering, University of Waterloo, N2L3G1, Waterloo, Ontario, Canada

    Paul H. Calamai

  3. Departamento de Matemática, Universidade de Coimbra, 3000, Coimbra, Portugal

    Joaquim J. Júdice

Authors
  1. Luis N. Vicente
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul H. Calamai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joaquim J. Júdice
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vicente, L.N., Calamai, P.H. & Júdice, J.J. Generation of disjointly constrained bilinear programming test problems. Comput Optim Applic 1, 299–306 (1992). https://doi.org/10.1007/BF00249639

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00249639

Keywords

Search

Navigation