petsc-3.7.1 2016-05-15
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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 Many br

Input Parameters

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

Output Parameters

FB -The Smoothed Fischer-Burmeister function vector Many br

Notes

The Smoothed Fischer-Burmeister function is defined as Many br
       phi(a,b) := sqrt(a*a + b*b + 2*mu*mu) - a - b
and is used reformulate a complementarity problem as a semismooth Many brsystem of equations. Many br

The result of this function is done by cases

l[i] == - infinity, u[i] == infinity -- fb[i] = -f[i] - 2*mu*x[i] Many br
l[i] == - infinity, u[i] finite -- fb[i] = phi(u[i]-x[i], -f[i], mu) Many br
l[i] finite, u[i] == infinity - - fb[i] = phi(x[i]-l[i], f[i], mu) Many br
l[i] finite < u[i] finite - - fb[i] = phi(x[i]-l[i], phi(u[i]-x[i], -f[u], mu), mu) Many br
otherwise l[i] == u[i] - - fb[i] = l[i] - x[i] Many br

Many br

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