Skip to main content
SpringerLink
Log in
Book cover

Constrained Global Optimization: Algorithms and Applications pp 75–83Cite as

Bilinear programming methods for nonconvex quadratic problems

  • Chapter
  • First Online:

  • 505 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 268))

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Al-Khayyal, F. and Falk, J.E. Jointly constrained biconvex programming. Math. of Oper. Res., Vol. 8, No. 2 (1983), 273–286.

    Google Scholar 

  2. Altman, M. Bilinear programming. Bull. Acad. Pol.Sci. Ser. Sci. Math. Astronom. Phy. 19 (1968), 741–746.

    Google Scholar 

  3. Czochralska, I. Bilinear programming. Zastosowania Mathematyki XVII, 3 (1982), 495–514.

    Google Scholar 

  4. Czochralska, I. The method of bilinear programming for nonconvex quadratic programming. Zastosowania Mathematyki XVII, 3 (1982), 515–525.

    Google Scholar 

  5. Gallo, G. and Ulkulu, A. Bilinear programming: An exact algorithm. Mathem. Progr. 12 (1971), 173–194.

    Article  Google Scholar 

  6. Konno, H. Bilinear programming: Part I. An algorithm for solving bilinear programs. Technical Report 71-9 (1971), Oper. Res., Stanford Univ.

    Google Scholar 

  7. Konno, H. Bilinear programming: Part II. Applications of bilinear programming. Technical Report 71-10 (1971), Oper. Res., Stanford Univ.

    Google Scholar 

  8. Konno, H. A cutting plane algorithm for solving bilinear programs. Math. Progr. 11 (1976), 14–27.

    Article  Google Scholar 

  9. Konno, H. Maximization of a convex quadratic function under linear constraints. Math. Progr. 11 (1976), 117–127.

    Article  Google Scholar 

  10. Konno, H. Maximizing a convex function over a hypercube. J. Oper. Res. Soc. Japan 23 (1980), 171–189.

    Google Scholar 

  11. Konno, H. An algorithm for solving bilinear knapsack problems. J. Oper. Res. Soc. Japan 24 (9181), 360–373.

    Google Scholar 

  12. Sherali, H. and Shetty, C.M. A finitely convergent algorithm for bilinear programming problems using polar cuts and disjunctive face cuts. Math. Progr. 19 (1980), 14–31.

    Article  Google Scholar 

  13. Thieu, T.V. Relationship between bilinear programming and concave minimization under linear constraints. Acta Math. Vietnam 5 (1980), 106–113.

    Google Scholar 

  14. Vaish, H. and Shetty C.M. The bilinear programming problem. Naval Res. Logist. Quarterly 23 (1976), 303–309.

    Google Scholar 

  15. Vaish, H. and Shetty C.M. A cutting plane algorithm for the bilinear programming problem. Naval Res. Logist. Quarterly 24 (1977), 83–94.

    Google Scholar 

Download references

Editor information

Panos M. Pardalos J. Ben Rosen

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this chapter

Cite this chapter

(1987). Bilinear programming methods for nonconvex quadratic problems. In: Pardalos, P.M., Rosen, J.B. (eds) Constrained Global Optimization: Algorithms and Applications. Lecture Notes in Computer Science, vol 268. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000042

Download citation

  • DOI: https://doi.org/10.1007/BFb0000042

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18095-1

  • Online ISBN: 978-3-540-47755-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation