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<div id="version" align=right><b>petsc-3.10.3 2018-12-18</b></div>
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<A NAME="VecSFischer"><H1>VecSFischer</H1></A>
Evaluates the Smoothed Fischer-Burmeister function for complementarity problems.
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
#include "petsctao.h"
<A HREF="../Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</A> <A HREF="../Tao/VecSFischer.html#VecSFischer">VecSFischer</A>(<A HREF="../Vec/Vec.html#Vec">Vec</A> X, <A HREF="../Vec/Vec.html#Vec">Vec</A> F, <A HREF="../Vec/Vec.html#Vec">Vec</A> L, <A HREF="../Vec/Vec.html#Vec">Vec</A> U, <A HREF="../Sys/PetscReal.html#PetscReal">PetscReal</A> mu, <A HREF="../Vec/Vec.html#Vec">Vec</A> FB)
</PRE>
Logically Collective on vectors
<P>
<H3><FONT COLOR="#CC3333">Input Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>X </B></TD><TD>- current point
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>F </B></TD><TD>- function evaluated at x
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>L </B></TD><TD>- lower bounds
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>U </B></TD><TD>- upper bounds
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>mu </B></TD><TD>- smoothing parameter
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Output Parameters</FONT></H3>
<DT><B>FB </B> -The Smoothed Fischer-Burmeister function vector
<br>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
The Smoothed Fischer-Burmeister function is defined as
<pre>
phi(a,b) := sqrt(a*a + b*b + 2*mu*mu) - a - b
</pre>
and is used reformulate a complementarity problem as a semismooth
system of equations.
<P>
<H3><FONT COLOR="#CC3333">The result of this function is done by cases</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>l[i] == </B></TD><TD>- infinity, u[i] == infinity -- fb[i] = -f[i] - 2*mu*x[i]
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>l[i] == </B></TD><TD>- infinity, u[i] finite -- fb[i] = phi(u[i]-x[i], -f[i], mu)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>l[i] finite, u[i] == infinity </B></TD><TD>- - fb[i] = phi(x[i]-l[i], f[i], mu)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>l[i] finite < u[i] finite </B></TD><TD>- - fb[i] = phi(x[i]-l[i], phi(u[i]-x[i], -f[u], mu), mu)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>otherwise l[i] == u[i] </B></TD><TD>- - fb[i] = l[i] - x[i]
</TD></TR></TABLE>
<P>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../Tao/VecFischer.html#VecFischer">VecFischer</A>()
<BR><P><B></B><H3><FONT COLOR="#CC3333">Level</FONT></H3>developer<BR>
<H3><FONT COLOR="#CC3333">Location</FONT></H3>
</B><A HREF="../../../src/tao/util/tao_util.c.html#VecSFischer">src/tao/util/tao_util.c</A>
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