#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 |
| FB | - The Fischer-Burmeister function vector |
phi(a,b) := sqrt(a*a + b*b) - a - b
and 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] |