Journal of Optimization Theory and Applications

, Volume 88, Issue 1, pp 139–155 | Cite as

Nonlinear complementarity as unconstrained optimization

  • C. Kanzow
Contributed Papers


Several methods for solving the nonlinear complementarity problem (NCP) are developed. These methods are generalizations of the recently proposed algorithms of Mangasarian and Solodov (Ref. 1) and are based on an unconstrianed minimization formulation of the nonlinear complementarity problem. It is shown that, under certain assumptions, any stationary point of the unconstrained objective function is already a solution of NCP. In particulr, these assumptions are satisfied by the mangasarian and Soolodov implicit Lagranian functioin. Furthermore, a special Newton-type method is suggested, and conditions for its local quadratic convergence are given. Finally, some preliminary numerical results are presented.

Key Words

Nonlinear complementarity problemjs unconstrained minimization Newton-type methods global minima stationary points 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • C. Kanzow
    • 1
  1. 1.Wissenschaftlicher Mitarbieiter, Institut für Angewandte MathematikUniversität HamburgHamburgGermany

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