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# VecSFischer

Evaluates the Smoothed Fischer-Burmeister function for complementarity problems.

### Synopsis

    #include "petsctao.h"
    PetscErrorCode VecSFischer(Vec X, Vec F, Vec L, Vec U, PetscReal mu, Vec FB)

Logically Collective on vectors

### Input Parameters

| X | - current point
| F | - function evaluated at x
| L | - lower bounds
| U | - upper bounds
| mu | - smoothing parameter

### Output Parameter

| FB | - The Smoothed Fischer-Burmeister function vector

### Notes

The Smoothed Fischer-Burmeister function is defined as

           phi(a,b) := sqrt(a*a + b*b + 2*mu*mu) - 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] - 2*mu*x[i]
| l[i] == | - infinity, u[i] finite -- fb[i] = phi(u[i]-x[i], -f[i], mu)
| l[i] finite, u[i] == infinity | - - fb[i] = phi(x[i]-l[i], f[i], mu)
| l[i] finite < u[i] finite | - - fb[i] = phi(x[i]-l[i], phi(u[i]-x[i], -f[u], mu), mu)
| otherwise l[i] == u[i] | - - fb[i] = l[i] - x[i]

### See Also

VecFischer()

### Level

developer

### Location

src/tao/util/tao_util.c
Index of all Tao routines
Table of Contents for all manual pages
Index of all manual pages