Skip to main content
SpringerLink
Log in

On V. Latorre and D.Y. Gao’s paper “Canonical duality for solving general nonconvex constrained problems”

  • Letter to the Editor
  • Published:
Optimization Letters Aims and scope Submit manuscript

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

Notes

  1. The reference [4] in the quoted text is D.Y. Gao’s book [1].

  2. The reference [7] is “Gao, D.Y.: Nonconvex semi-linear problems and canonical duality solutions, in Advances in Mechanics and Mathematics II. In: Gao, D.Y., Ogden R.W. (eds.), pp. 261–311. Kluwer Academic Publishers (2003)”.

  3. The reference [28] is our paper [10].

  4. The reference [6] is “Gao, D.Y.: Perfect duality theory and complete set of solutions to a class of global optimization problems. Optimization 52, 467–493 (2003)”, while for the reference [7] see the footnote\(^{2}\).

References

  1. Gao, D.Y.: Duality Principles in Nonconvex System: Theory, Methods and Applications. Kluwer Academic Publishers, Dordrecht (2000)

    Book  MATH  Google Scholar 

  2. Gao, D.Y., Strang, G.: Geometric nonlinearity: potential energy, complementary energy, and the gap function. Q. Appl. Math. 47, 487–504 (1989)

    MathSciNet  MATH  Google Scholar 

  3. Gao, D.Y., Wu, C.: On the triality theory in global optimization (I) unconstrained problems. arXiv:1104.2970v1 [math.OC] (2011)

  4. Gao, D.Y., Wu, C.: Triality theory for general unconstrained global optimization problems. arXiv:1104.2970v2 [math.OC] (2012)

  5. Latorre, V., Gao, D.Y.: Canonical duality for solving general nonconvex constrained problems. Optim. Lett. doi:10.1007/s11590-015-0860-0

  6. Strugariu, R., Voisei, M.D., Zălinescu, C.: Counter-examples in bi-duality, triality and tri-duality. Discrete Contin. Dyn. Syst. Ser. A (DCDS-A) 31, 1453–1468 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Voisei, M.D., Zălinescu, C.: On three duality results. arXiv:1008.4329 (2010)

  8. Voisei, M.D., Zălinescu, C.: Counterexamples to a triality theorem in “Canonical dual least square method”. Comput. Optim. Appl. 50, 619–628 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Voisei, M.D., Zălinescu, C.: A counter-example to ‘Minimal distance between two non-convex surfaces’. Optimization 60, 593–602 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Voisei, M.D., Zălinescu, C.: Some remarks concerning Gao–Strang’s complementary gap function. Appl. Anal. 90, 1111–1121 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Voisei, M.D., Zălinescu, C.: Counterexamples to some triality and tri-duality results. J. Global Optim. 49, 173–183 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Voisei, M.D., Zălinescu, C.: On D.Y. Gao and R.W. Ogden’s paper “Multiple solutions to non-convex variational problems with implications for phase transitions and numerical computation”. arXiv:1101.3534 [math.OC] (2011)

  13. Voisei, M.D., Zălinescu, C.: A non-convex variational problem appearing in a large deformation elasticity problem. arXiv:1202.3515 [math.OC] (2012)

  14. Voisei, M.D., Zălinescu, C.: Counterexamples to a triality theorem for quadratic-exponential minimization problems. Math. Methods Oper. Res. 77(2), 227–237 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zălinescu, C.: On two triality results. Optim. Eng. 12, 477–487 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zălinescu, C.: On the paper “A study on concave optimization via canonical dual function”. arXiv:1112.2130 [math.OC] (2011)

Download references

Acknowledgments

I would like to thank the two anonymous referees, as well as Prof. P. Krokhmal, for their remarks which led to the present form of this letter.

Author information

Authors and Affiliations

  1. Faculty of Mathematics, University “Al. I. Cuza” Iaşi, Iaşi, Romania

    C. Zălinescu

  2. “O. Mayer” Institute of Mathematics of the Romanian Academy, Iaşi, Romania

    C. Zălinescu

Authors
  1. C. Zălinescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Zălinescu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zălinescu, C. On V. Latorre and D.Y. Gao’s paper “Canonical duality for solving general nonconvex constrained problems”. Optim Lett 10, 1781–1787 (2016). https://doi.org/10.1007/s11590-016-1033-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-016-1033-5

Keywords

Search

Navigation