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A semismooth equation approach to the solution of nonlinear complementarity problems

Abstract

In this paper we present a new algorithm for the solution of nonlinear complementarity problems. The algorithm is based on a semismooth equation reformulation of the complementarity problem. We exploit the recent extension of Newton's method to semismooth systems of equations and the fact that the natural merit function associated to the equation reformulation is continuously differentiable to develop an algorithm whose global and quadratic convergence properties can be established under very mild assumptions. Other interesting features of the new algorithm are an extreme simplicity along with a low computational burden per iteration. We include numerical tests which show the viability of the approach.

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Correspondence to Francisco Facchinei.

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De Luca, T., Facchinei, F. & Kanzow, C. A semismooth equation approach to the solution of nonlinear complementarity problems. Mathematical Programming 75, 407–439 (1996). https://doi.org/10.1007/BF02592192

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Key words

  • Nonlinear complementarity problem
  • Semismoothness
  • Smooth merit function
  • Global convergence
  • Quadratic convergence