## Complementarity and Variational Problems: State of the ArtAfter more than three decades of research, the subject of complementarity problems and its numerous extensions has become a well-established and fruitful discipline within mathematical programming and applied mathematics. Sources of these problems are diverse and span numerous areas in engineering, economics, and the sciences. Includes refereed articles. |

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### Contents

On the Existence of Solutions to Complementarity | 12 |

The Extended Linear Complementarity Problem and | 22 |

Crash Techniques for LargeScale Complementarity | 40 |

Noncooperative Games in Networks Stability | 62 |

A Semismooth Newton Method for Variational | 76 |

Minimizing and Stationary Sequences of Merit Functions | 91 |

Smoothing of Mixed Complementarity Problems | 105 |

On the PseudoLipschitzian Behavior of the Inverse of | 117 |

Overlapping Block Methods for Obstacle Problems with | 165 |

A Merit Function and a NewtonType Method | 181 |

VII | 194 |

A New Class of Merit Functions for the Nonlinear | 204 |

The IllPosed Linear Complementarity Problem | 226 |

Least Elements and the Minimal Rank Matrices | 259 |

Linear Complementarity and Discounted Polystochastic | 284 |

A Truncated Newton InteriorPoint Algorithm for | 315 |

Steady Sliding and Linear Complementarity | 132 |

A Nonsmooth Approach to Optimization Problems with | 148 |

Superlinear Convergence of an InteriorPoint Method | 345 |

### Common terms and phrases

affine function algebraic algorithm analysis Applications assume assumptions block relaxation methods boundedness components computational condition cone consider constant constraints continuously differentiable convergence convex corresponding defined denote diagonal domain domain decomposition methods dynamics ELCP element equations equilibrium equivalent error bounds example exists fail fail fail finite formulation friction given global Hence holds implies index set interior-point iteration Jacobian KANZOW Lemma level sets linear complementarity problem linear system Lipschitz continuous Lipschitzian Ma(x mapping Math Mathematical Programming matrix merit function minimization mixed complementarity problem monotone Newton method nodes nonempty nonlinear complementarity problems nonnegative nonsingular nonsmooth numerical obstacle problem obtain optimization overlapping block P-matrix Pa(x Pang parameter positive definite positive semi-definite Proof properties prove quadratic program regular RLCP satisfies semismooth sequence SIAM solving stationary point step subdomains subproblem subset superlinear symmetric technique Theorem unique variational inequality vector zero