#include "petsctao.h" PetscErrorCode VecFischer(Vec X, Vec F, Vec L, Vec U, Vec FB)Logically Collective on vectors

X | - current point | |

F | - function evaluated at x | |

L | - lower bounds | |

U | - upper bounds |

phi(a,b) := sqrt(a*a + b*b) - a - band is used reformulate a complementarity problem as a semismooth system of equations.

l[i] == | - infinity, u[i] == infinity -- fb[i] = -f[i] | |

l[i] == | - infinity, u[i] finite -- fb[i] = phi(u[i]-x[i], -f[i]) | |

l[i] finite, u[i] == infinity | - - fb[i] = phi(x[i]-l[i], f[i]) | |

l[i] finite < u[i] finite | - - fb[i] = phi(x[i]-l[i], phi(u[i]-x[i], -f[u])) | |

otherwise l[i] == u[i] | - - fb[i] = l[i] - x[i] |

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