Skip to main content
Log in

On two triality results

  • Published:
Optimization and Engineering Aims and scope Submit manuscript

Abstract

In this note counter-examples to two triality results are provided. In addition, one of the before mentioned results is corrected and improved.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Gao DY (1999) General analytic solutions and complementary variational principles for large deformation nonsmooth mechanics. Meccanica 34:169–198

    MathSciNet  MATH  Google Scholar 

  • Gao DY (2000a) Duality Principles in Nonconvex Systems: Theory, Methods and Applications. Kluwer Academic, Dordrecht

    MATH  Google Scholar 

  • Gao DY (2000b) Canonical dual transformation method and generalized triality theory in nonsmooth global optimization. J Glob Optim 17:127–160

    Article  MATH  Google Scholar 

  • Gao DY (2003) Perfect duality theory and complete solutions to a class of global optimization problems. Optimization 52:467–493

    Article  MathSciNet  MATH  Google Scholar 

  • Gao DY (2004) Canonical duality theory and solutions to constrained nonconvex quadratic programming. J Glob Optim 29:377–399

    Article  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Liu J, Gao DY, Gao Y (2009) Canonical duality for solving nonconvex and nonsmooth optimization problem. Optim Eng 10:153–165

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang X, Zhu J, Gao DY (2009) Solution to nonconvex quadratic programming with both inequality and box constraints. Optim Eng 10:183–191

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Constantin Zălinescu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zălinescu, C. On two triality results. Optim Eng 12, 477–487 (2011). https://doi.org/10.1007/s11081-010-9134-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11081-010-9134-y

Keywords

Navigation