Newton-Like Methods

  • G. Isac
  • V. A. Bulavsky
  • V. V. Kalashnikov
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 63)


This chapter deals with the problem of finding out an equilibrium in an oligopolistic market model where several subjects supply a single homogeneous product in a non-cooperative manner. The problem is reduced to a nonlinear equation some terms of which are determined by solving nonlinear complementarity problems. An algorithm is presented that combines the Newton method steps with the dichotomy techniques. Under certain assumptions, the algorithm is shown to be convergent at the quadratic rate. Finally, the algorithm is extended to the case of nonlinear production costs, and its linear convergence is demonstrated.


Newton Method Complementarity Problem Linear Complementarity Problem Nonlinear Complementarity Problem Inverse Demand Function 
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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • G. Isac
    • 1
  • V. A. Bulavsky
    • 2
  • V. V. Kalashnikov
    • 2
  1. 1.Department of Mathematics and Computer ScienceRoyal Military College of CanadaKingstonCanada
  2. 2.Central Economics Institute (CEMI) of Russian Academy of SciencesMoscowRussia

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