Skip to main content
SpringerLink
Log in

Generalizations of Interior Point Methods for the Linear Complementarity Problem

  • Reference work entry
Encyclopedia of Optimization

  • 160 Accesses

Article Outline

Introduction

Definitions

Formulation

  An Interior Point Reduction Algorithm to Solve the LCP

  An Interior Point Potential Algorithm to Solve General LCPs

Methods and Applications

Models

  An Interior Point Newton Method for the General LCP

  Generalization of an Interior Point Reduction Algorithm to Solve General LCPs

Cases

Conclusions

See also

References

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 2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 2,499.99
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

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  2. Cottle RW, Dantzig G (1968) Complementarity pivot theory of mathematical programming. Lin Algebra Appl 1:103–125

    Article  MathSciNet  MATH  Google Scholar 

  3. Cottle RW, Pang J-S, Stone RE (1992) The Linear Complementarity Problem. Academic Press, Inc., San Diego

    Google Scholar 

  4. Kojima M, Megiddo N, Ye Y (1992) An Interior point potential reduction algorithm for the linear complementarity problem. Math Programm 54:267–279

    Article  MathSciNet  MATH  Google Scholar 

  5. Lemke CE (1965) Bimatrix Equilibrium Points and Mathematical Programming. Manag Sci 11:123–128

    Article  MathSciNet  Google Scholar 

  6. Lemke CE, Howson JT (1964) Equilibrium points of bimatrix games. SIAM J Appl Math 12:413–423

    Article  MathSciNet  MATH  Google Scholar 

  7. Mangasarian OL (1979) Simplified characterizations of linear complementarity problems solvable as linear programs. Math Programm 10(2):268–273

    MathSciNet  Google Scholar 

  8. Mangasarian OL (1976) Linear complementarity problems solvable by a single linear program. Math Programm 10:263–270

    Article  MathSciNet  MATH  Google Scholar 

  9. Mangasarian OL (1978) Characterization of linear co complementarity problems as linear program. Math Programm 7:74–87

    MATH  Google Scholar 

  10. Ferris MC, Sinapiromsaran K (2000) Formulating and Solving Nonlinear Programs as Mixed Complementarity Problems. In: Nguyen VH, Striodot JJ, Tossing P (eds) Optimization. Springer, Berlin, pp 132–148

    Google Scholar 

  11. Patrizi G (1991) The Equivalence of an LCP to a Parametric Linear program with a Scalar Parameter. Eur J Oper Res 51:367–386

    Article  MATH  Google Scholar 

  12. Vavasis S (1991) Nonlinear Optimization: Complexity Issues. Oxford University Press, Oxford

    MATH  Google Scholar 

  13. Ye Y (1991) An \( { O(n^3L) } \) Potential Reduction Algorithm for linear Programming. Math Programm 50:239–258

    Article  MATH  Google Scholar 

  14. Ye Y (1992) On affine scaling algorithms for nonconvex quadratic programming. Math Programm 56:285–300

    Article  Google Scholar 

  15. Ye Y (1993) A fully polynomial-time approximation algorithm for computing a stationary point of the general linear complementarity problem. Math Oper Res 18:334–345

    Article  MathSciNet  MATH  Google Scholar 

  16. Ye Y, Pardalos PM (1991) A Class of Linear Complementarity Problems Solvable in Polynomial Time. Lin Algebra Appl 152:3–17

    Article  MathSciNet  MATH  Google Scholar 

  17. Ye Y (1997) Interior Point Algorithms: Theory and Analysis. Wiley, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza”, Rome, Italy

    Laura Di Giacomo

Authors
  1. Laura Di Giacomo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Di Giacomo, L. (2008). Generalizations of Interior Point Methods for the Linear Complementarity Problem . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_199

Download citation

Publish with us

Policies and ethics

Search

Navigation