Skip to main content
SpringerLink
Log in

An algorithm for computing all solutions of an absolute value equation

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

Presented is an algorithm which in a finite (but exponential) number of steps computes all solutions of an absolute value equation Ax + B|x| = b (A, B square), or fails. Failure has never been observed for randomly generated data. The algorithm can also be used for computation of all solutions of a linear complementarity problem.

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. Fiedler M., Nedoma J., Ramík J., Rohn J., Zimmermann K.: Linear optimization problems with inexact data. Springer-Verlag, New York (2006)

    MATH  Google Scholar 

  2. Mangasarian O.: Absolute value equation solution via concave minimization. Optim. Lett. 1(1), 3–8 (2007). doi:10.1007/s11590-006-0005-6

    Article  MathSciNet  MATH  Google Scholar 

  3. Mangasarian O.: Absolute value programming. Comput. Optim. Appl. 36(1), 43–53 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Mangasarian O.L.: A generalized Newton method for absolute value equations. Optim. Lett. 3(1), 101–108 (2009). doi:10.1007/s11590-008-0094-5

    Article  MathSciNet  MATH  Google Scholar 

  5. Mangasarian O.L., Meyer R.R.: Absolute value equations. Linear Algebra Appl. 419(2–3), 359–367 (2006). doi:10.1016/j.laa.2006.05.004

    Article  MathSciNet  MATH  Google Scholar 

  6. Murty K.G.: Linear complementarity, linear and nonlinear programming. Heldermann, Berlin (1988)

    MATH  Google Scholar 

  7. Pardalos P.: Linear complementarity problems solvable by integer programming. Optimization 19(4), 467–474 (1988). doi:10.1080/02331938808843365

    Article  MathSciNet  MATH  Google Scholar 

  8. Pardalos, P.M.: The linear complementarity problem. In: Gomez, S. et al. (eds) Advances in optimization and numerical analysis. Proceedings of the 6th workshop on optimization and numerical analysis, Oaxaca, Mexico, January 1992. Dordrecht: Kluwer Academic Publishers. Math. Appl. Dordr. 275, 39–49 (1994)

  9. Prokopyev O.: On equivalent reformulations for absolute value equations. Comput. Optim. Appl 44(3), 363–372 (2009). doi:10.1007/s10589-007-9158-1

    Article  MathSciNet  MATH  Google Scholar 

  10. Rohn J.: Systems of linear interval equations. Linear Algebra Appl. 126, 39–78 (1989). doi:10.1016/0024-3795(89)90004-9

    Article  MathSciNet  MATH  Google Scholar 

  11. Rohn, J.: An algorithm for solving the absolute value equation. Electron. J. Linear Algebra 18, 589–599 (2009). http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol18_pp589-599.pdf

  12. Rohn, J.: An algorithm for solving the absolute value equation: An improvement. Technical Report 1063, Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague (2010). http://uivtx.cs.cas.cz/~rohn/publist/absvaleqnreport.pdf

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic

    Jiri Rohn

  2. School of Business Administration, Anglo-American University, Prague, Czech Republic

    Jiri Rohn

Authors
  1. Jiri Rohn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiri Rohn.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rohn, J. An algorithm for computing all solutions of an absolute value equation. Optim Lett 6, 851–856 (2012). https://doi.org/10.1007/s11590-011-0305-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-011-0305-3

Keywords

Search

Navigation