Skip to main content
SpringerLink
Log in

Dual form reduction in the atomic optimization method

  • Large Scale Systems Control
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

One-dimensional optimization problems with a polynomial objective function and polynomial matrix inequality constraints are considered. For problems dual to their linear relaxations, a transformation is presented that makes them compatible with the atomic optimization method, both in its basic and in the generalized form with a reduced number of atoms.

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

Similar content being viewed by others

References

  1. Pozdyayev, V.V., Atomic Optimization, I. Search Space Transformation and One-Dimensional Problems, Autom. Remote Control, 2013, vol. 74, no. 12, pp. 2069–2092.

    Article  MathSciNet  MATH  Google Scholar 

  2. Pozdyayev, V.V., Atomic Optimization, II. Multidimensional Problems and Polynomial Matrix Inequalities, Autom. Remote Control, 2014, vol. 75, no. 6, pp. 1155–1171.

    Article  MathSciNet  MATH  Google Scholar 

  3. Pozdyayev, V.V., Primal and Dual Forms for the Atomic Optimization Method and 1D Problems, Dinamika Slozhn. Sist.—XXI Vek, 2014, no. 1, pp. 53–58.

    Google Scholar 

  4. Henrion, D. and Lasserre, J.-B., Detecting Global Optimality and Extracting Solutions in GloptiPoly, in Positive Polynomials in Control, Lecture Notes in Control and Information Science, vol. 312, Henrion, D. and Garulli, A., Eds., Berlin: Springer-Verlag, 2005, pp. 293–310.

    Chapter  Google Scholar 

  5. Henrion, D. and Lasserre, J.-B., Convergent Relaxations of Polynomial Matrix Inequalities and Static Output Feedback, IEEE Trans. Autom. Control, 2006, vol. 51, no. 2, pp. 192–202.

    Article  MathSciNet  Google Scholar 

  6. Henrion, D., Lasserre, J.-B., and Löfberg, J., GloptiPoly 3: Moments, Optimization and Semidefinite Programming, Optimiz. Meth. Software, 2009, vol. 24, no. 4–5, pp. 761–779.

    Google Scholar 

  7. Lasserre, J.-B., Global Optimization with Polynomials and the Problem of Moments, SIAM J. Optimiz., 2001, vol. 11, no. 3, pp. 796–817.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Arzamas Polytechnic Institute of Alekseev Nizhny Novgorod State Technical University, Arzamas, Russia

    V. V. Pozdyayev

Authors
  1. V. V. Pozdyayev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Pozdyayev.

Additional information

Original Russian Text © V.V. Pozdyayev, 2015, published in Upravlenie Bol’shimi Sistemami, 2015, No. 54, pp. 66–85.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pozdyayev, V.V. Dual form reduction in the atomic optimization method. Autom Remote Control 78, 940–952 (2017). https://doi.org/10.1134/S0005117917050150

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117917050150

Search

Navigation