Skip to main content


  • Chapter
  • First Online:
Scalable Algorithms for Contact Problems

Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 36))

  • 787 Accesses


In this chapter, we briefly review the results concerning the minimization of quadratic functions to the extent which is sufficient for understanding the algorithms described in Part II. The results are presented with specialized arguments, typically algebraic, that exploit the specific structure of these problems. Systematic exposition of optimization theory in the framework of nonlinear optimization can be found in the books by Bertsekas (Nonlinear Optimization, 1999, [1]), Nocedal and Wright (Numerical Optimization, 2000, [2]), Conn, Gould, and Toint (Trust Region Methods, 2000, [3]), Bazaraa, Sherali, and Shetty (Nonlinear Programming, Theory and Algorithms, 1993, [4]), or Griva, Nash, and Sofer (Linear and Nonlinear Optimization, 2009, [5]).

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

Access this chapter

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Similar content being viewed by others


  1. Bertsekas, D.P.: Nonlinear Optimization. Athena Scientific, Belmont (1999)

    MATH  Google Scholar 

  2. Nocedal, J., Wright, S.F.: Numerical Optimization. Springer, New York (2000)

    MATH  Google Scholar 

  3. Conn, A.R., Gould, N.I.M., Toint, Ph.L: Trust Region Methods. SIAM, Philadelphia (2000)

    Google Scholar 

  4. Bazaraa, M.S., Shetty, C.M., Sherali, H.D.: Nonlinear Programming, Theory and Algorithms, 2nd edn. Wiley, New York (1993)

    MATH  Google Scholar 

  5. Griva, I., Nash, S.G., Sofer, A.: Linear and Nonlinear Optimization. SIAM, Philadelphia (2009)

    Book  MATH  Google Scholar 

  6. Frank, M., Wolfe, P.: An algorithm for quadratic programming. Naval Research Logistic Quarterly 3, 95–110 (1956)

    Article  MathSciNet  Google Scholar 

  7. Dostál, Z.: On solvability of convex non-coercive quadratic programming problems. JOTA 143(2), 413–416 (2009)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Zdeněk Dostál .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media LLC

About this chapter

Cite this chapter

Dostál, Z. (2016). Optimization. In: Scalable Algorithms for Contact Problems. Advances in Mechanics and Mathematics, vol 36. Springer, New York, NY.

Download citation

Publish with us

Policies and ethics