Skip to main content
SpringerLink
Log in

Local Convergence of Sequential Convex Programming for Nonconvex Optimization

  • Conference paper
  • First Online:
Recent Advances in Optimization and its Applications in Engineering

Summary

This paper introduces sequential convex programming (SCP), a local optimzation method for solving nonconvex optimization problems. A full-step SCP algorithm is presented. Under mild conditions the local convergence of the algorithm is proved as a main result of this paper. An application to optimal control illustrates the performance of the proposed algorithm.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Boyd and L. Vandenberghe (2004). Convex optimization. University Press, Cambridge.

    MATH  Google Scholar 

  2. R. Correa and H. Ramirez C (2004). A global algorithm for nonlinear semidefinite programming. SIAM J. Optim., 15(1):303–318.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. L. Dontchev and T. R. Rockafellar (1996). Characterizations of strong regularity for variational inequalities over polyhedral convex sets. SIAM J. Optim., 6(4):1087–1105.

    Article  MATH  MathSciNet  Google Scholar 

  4. B. Fares, D. Noll, and P. Apkarian (2002). Robust control via sequential semidefinite programming. SIAM J. Control Optim., 40:1791–1820.

    Article  MATH  MathSciNet  Google Scholar 

  5. R. W. Freund, F. Jarre, and C. H. Vogelbusch (2007). Nonlinear semidefinite programming: sensitivity, convergence, and an application in passive reduced-order modeling. Mathemat- ical Programming, Ser. B, 109:581–611.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Fukushima, Z.-Q. Luo, and P. Tseng (2003). A sequential quadratically constrained quadratic programming method for differentiable convex minimization. SIAM J. Optimization, 13(4):1098–1119.

    Article  MATH  MathSciNet  Google Scholar 

  7. H. Jaddu (2002). Direct solution of nonlinear optimal control problems using quasilinearization and Chebyshev polynomials. Journal of the Franklin Institute, 339:479–498.

    Article  MATH  MathSciNet  Google Scholar 

  8. F. Jarre (2003). On an approximation of the Hessian of the Lagrangian. Optimization Online (http://www.optimization-online.org/DB_HTML/2003/12/800.html).

  9. J.L. Junkins and J.D. Turner (1986). Optimal spacecraft rotational maneuvers. Elsevier, Amsterdam.

    Google Scholar 

  10. C. Kanzow, C. Nagel, H. Kato and M. Fukushima (2005). Successive linearization methods for nonlinear semidefinite programs. Computational Optimization and Applications, 31:251–273.

    Article  MATH  MathSciNet  Google Scholar 

  11. D. Klatte and B. Kummer (2001). Nonsmooth equations in optimization: regularity, cal- culus, methods and applications. Springer-Verlag, New York.

    Google Scholar 

  12. A. S. Lewis and S. J. Wright (2008). A proximal method for composite minimization. http://arxiv.org/abs/0812.0423

  13. S. M. Robinson (1980). Strong regularity generalized equations, Mathematics of Operation Research, 5(1):43–62.

    Article  MATH  Google Scholar 

  14. R. T. Rockafellar and R. J-B. Wets (1997). Variational analysis. Springer-Verlag, New York.

    Google Scholar 

Download references

Acknowledgments

This research was supported by Research Council KUL: CoE EF/05/006 Optimization in Engineering(OPTEC), GOA AMBioRICS, IOF-SCORES4CHEM, several PhD/postdoc & fellow grants; the Flemish Government via FWO: PhD/postdoc grants, projects G.0452.04, G.0499.04, G.0211.05, G.0226.06, G.0321.06, G.0302.07, G.0320.08 (convex MPC), G.0558.08 (Robust MHE), G.0557.08, G.0588.09, research communities (ICCoS, ANMMM, MLDM) and via IWT: PhD Grants, McKnow-E, Eureka-Flite+EU: ERNSI; FP7-HD-MPC (Collaborative Project STREP-grantnr. 223854), Erbocon, Contract Research: AMINAL, and Helmholtz Gemeinschaft: viCERP; Austria: ACCM, and the Belgian Federal Science Policy Office: IUAP P6/04 (DYSCO, Dynamical systems, control and optimization, 2007-2011).

The authors are very much thankful to the anonymous referees, who corrected numerous mistakes and suggested several improvements.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering (SCD-ESAT) and OPTEC, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, 3001, Heverlee, Belgium

    Quoc Tran Dinh & Moritz Diehl

Authors
  1. Quoc Tran Dinh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Moritz Diehl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Quoc Tran Dinh .

Editor information

Editors and Affiliations

  1. Dept. Electrical Engineering (ESAT), Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, Leuven, 3001, Belgium

    Moritz Diehl

  2. CORE-UCL, Voie du Roman Pays 34, Louvain-la-Neuve, 1348, Belgium

    Francois Glineur

  3. , Department Computerwetenschappen, Katholieke Universiteit Leuven, Leuven, 3001, Belgium

    Elias Jarlebring

  4. Dept. Computer Science, Katholieke Universiteit Leuven, Celesijnenlaan 200a, Leuven, 3001, Belgium

    Wim Michiels

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer -Verlag Berlin Heidelberg

About this paper

Cite this paper

Dinh, Q.T., Diehl, M. (2010). Local Convergence of Sequential Convex Programming for Nonconvex Optimization. In: Diehl, M., Glineur, F., Jarlebring, E., Michiels, W. (eds) Recent Advances in Optimization and its Applications in Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12598-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12598-0_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12597-3

  • Online ISBN: 978-3-642-12598-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation