Optimization Letters

, Volume 6, Issue 2, pp 363–373 | Cite as

Solution existence and stability of quadratically constrained convex quadratic programs

  • D. S. KimEmail author
  • N. N. Tam
  • N. D. Yen
Original Paper


We propose verifiable necessary and sufficient conditions for the solution existence of a convex quadratic program whose constraint set is defined by finitely many convex linear-quadratic inequalities. A related stability analysis of the problem is also considered.


Convex quadratic program Solution existence Recession cone Eaves-type theorem Stability analysis 


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  1. 1.
    Anstreicher K.M.: Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming. J. Glob. Optim. 43, 471–484 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Belousov E.G.: Introduction to Convex Analysis and Integer Programming. Moscow University Publ., Moscow (1977) (in Russian)zbMATHGoogle Scholar
  3. 3.
    Belousov E.G., Klatte D.: A Frank–Wolfe type theorem for convex polynomial programs. Comput. Optim. Appl. 22, 37–48 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Bertsekas D.P.: Nonlinear Programming, 2nd edn. Athena Scientific, Belmont (2003)Google Scholar
  5. 5.
    Dostál Z.: On solvability of convex noncoercive quadratic programming problems. J. Optim. Theory Appl. 143, 413–416 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Eaves B.C.: On quadratic programming. Manag. Sci. 17, 698–711 (1971)zbMATHCrossRefGoogle Scholar
  7. 7.
    Lee G.M., Tam N.N., Yen N.D.: Quadratic Programming and Affine Variational Inequalities: A Qualitative Study, Series: “Nonconvex Optimization and Its Applications”, vol. 78. Springer, New York (2005)Google Scholar
  8. 8.
    Luo Z.-Q., Zhang S.: On extensions of the Frank–Wolfe theorems. Comput. Optim. Appl. 13, 87–110 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Raber U.: A simplicial branch-and-bound method for solving nonconvex all-quadratic programs. J. Glob. Optim. 13, 417–432 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Robinson S.M.: Generalized equations and their solutions: Part I, Basic theory. Math. Program. Study 10, 128–141 (1979)zbMATHGoogle Scholar
  11. 11.
    Rockafellar R.T.: Convex Analysis. Princeton University Press, Princeton (1970)zbMATHGoogle Scholar
  12. 12.
    Terlaky T.: On l p programming. Eur. J. Oper. Res. 22, 70–100 (1985)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Applied MathematicsPukyong National UniversityPusanKorea
  2. 2.Department of MathematicsHanoi Pedagogical Institute No. 2Vinh PhucVietnam
  3. 3.Institute of MathematicsVietnamese Academy of Science and TechnologyHanoiVietnam

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