petsc-3.12.5 2020-03-29

VecSFischer

Evaluates the Smoothed Fischer-Burmeister function for complementarity problems.

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

Logically Collective on vectors

FB -The Smoothed Fischer-Burmeister function vector

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.

	l[i] ==	- infinity, u[i] == infinity -- fb[i] = -f[i] - 2mux[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]

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