petsc-master 2016-02-13
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Evaluates the Fischer-Burmeister function for complementarity problems.


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

Input Parameters

X - current point
F - function evaluated at x
L - lower bounds
U - upper bounds

Output Parameters

FB -The Fischer-Burmeister function vector


The Fischer-Burmeister function is defined as
       phi(a,b) := sqrt(a*a + b*b) - a - b
and is used reformulate a complementarity problem as a semismooth system of equations.

The result of this function is done by cases

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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