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Nonconvex quadratic programs, linear complementarity problems, and integer linear programs

  • F. Giannessi
  • E. Tomasin
Mathematical Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3)

Abstract

The problem of nonconvex quadratic programs is considered, and an algorithm is proposed to find the global minimum, solving the correspon ding linear complementarity problem. An application to the general complementarity problem and to 0–1 integer programming problems, is shown.

Keywords

Programming Problem Quadratic Programming Complementarity Problem Linear Complementarity Problem Complementarity Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    -ABADIE J., On the Khun-Tucker Theorem. In "Nonlinear programming", J.Abadie (ed.), North-Holland Publ. Co., 1967, pp. 19–36.Google Scholar
  2. [2]
    -BEALE E.M.L., Numericae Methods. In "Nonlinear Programming", J.Aba die (ed.), North-Holland Publ. Co., 1967, pp. 133–205.Google Scholar
  3. [3]
    -BURDET C.A., General Quadratic Programming. Carnegie-Mellon Univ. Paper W.P.-41-71-2, Nov. 1971.Google Scholar
  4. [4]
    -COTTLE R. W., The principal pivoting method of quadratic programming. In "Mathematics of the decision sciences, Part I, eds. G.B.Dantzig and A.F.Veinott Jr. American Mathematical Society, Providence, 1968, pp. 144–162.Google Scholar
  5. [5]
    -COTTLE R.W. and W.C. MYLANDER, Ritter's cutting plane method for nonconvex quadratic programming. In "Integer and nonlinear programming", J;Abadie (ed.), North-Holland Publ. Co., 1970, pp.257–283.Google Scholar
  6. [6]
    -DANTZIG C.B., Linear Programming and Extension. Princeton Univ. Press, 1963.Google Scholar
  7. [6a]
    -DANTZIG G.B., A.F. VEINOTT, Mathematics of the Decision Sciences. American Mathematical Society, Providence, 1968.Google Scholar
  8. [7]
    -EAVES B.C., On the basic theorem of complementarity. "Mathematical Programming", Vol.1, 1971, n. 1, pp.68–75.CrossRefGoogle Scholar
  9. [8]
    -GIANNESSI F., Nonconvex quadratic programming, linear complementarity problems, and integer linear programs. Dept. of Operations Research and Statistical Sciences, Univ. of PISA, ITALY. Paper A/1, January 1973.Google Scholar
  10. [9]
    -KARAMARDIAN S., The complementarity problem. "Mathematical Programming", Vol.2, 1972, n. 1, pp. 107–123.CrossRefGoogle Scholar
  11. [10]
    -KUHN H.W. and A.W. TUCKER, Nonlinear programming. In: "Second Berkeley Symp. Mathematical Statistics and Probability", ed. J. Neyman, Univ. of California Press, Berkeley, 1951, pp.481–492.Google Scholar
  12. [11]
    -LEMKE C.E., Bimatrix Equilibrium Points and Mathematical Programming. "Management Science", Vol.11, 1965, pp.681–689.Google Scholar
  13. [12]
    -RAGHAVACHARI M., On connections between zero-one integer programming and concave programming under linear constraints.Google Scholar
  14. [13]
    -RITTER K., A method for solving maximum problems with a nonconcave quadratic objective function. Z.Wharscheinlichkeitstheorie, Vern. Geb. 4, 1966, pp. 340–351.Google Scholar
  15. [14]
    -TOMASIN E., Global optimization in nonconvex quadratic programming and related lields. Dept. of Operations Research and Statistical Scien ces, Univ. of Pisa, September 1973.Google Scholar
  16. [15]
    -TUI HOANG, Concave programming under linear constraints. Soviet Math., 1964, pp.1437–1440.Google Scholar
  17. [16]
    -ZWART P.B. Nonlinear programming: Counter examples to global optimization algorithms proposed by Ritter and Tui. Washington Univ., Dept. of Applied Mathematics and Computer Sciences School of Ingeeniring and Applied Science. Report No. Co-1493-32-1972.Google Scholar
  18. [17]
    -BURDET The lacial decomposition method. Graduate School of Industrial Administration Carnegie Mellon Univ. Pittsbrgh, Penn. May 1972.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  • F. Giannessi
    • 1
  • E. Tomasin
    • 2
  1. 1.Department of Operations Research and Statistical SciencesUniv. of PISAPisaItaly
  2. 2.Mathematical InstituteCa' Foscari UniversityVeniceItaly

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