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<div id="version" align=right><b>petsc-3.7.5 2017-01-01</b></div>
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<A NAME="KSPNASH"><H1>KSPNASH</H1></A>
Code to run conjugate gradient method subject to a constraint on the solution norm. This is used in Trust Region methods for nonlinear equations, <A HREF="../SNES/SNESNEWTONTR.html#SNESNEWTONTR">SNESNEWTONTR</A>
<H3><FONT COLOR="#CC3333">Options Database Keys</FONT></H3>
<DT><B>-ksp_nash_radius <r> </B> -Trust Region Radius
<br>
<P>
Notes: This is rarely used directly
<P>
<P>
Use preconditioned conjugate gradient to compute
an approximate minimizer of the quadratic function
<P>
q(s) = g^T * s + 0.5 * s^T * H * s
<P>
subject to the trust region constraint
<P>
|| s || <= delta,
<P>
where
<P>
delta is the trust region radius,
g is the gradient vector,
H is the Hessian approximation, and
M is the positive definite preconditioner matrix.
<P>
<A HREF="../KSP/KSPConvergedReason.html#KSPConvergedReason">KSPConvergedReason</A> may be
<pre>
KSP_CONVERGED_CG_NEG_CURVE if convergence is reached along a negative curvature direction,
</pre>
<pre>
KSP_CONVERGED_CG_CONSTRAINED if convergence is reached along a constrained step,
</pre>
<pre>
other <A HREF="../KSP/KSP.html#KSP">KSP</A> converged/diverged reasons
</pre>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
The preconditioner supplied should be symmetric and positive definite.
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../KSP/KSPCreate.html#KSPCreate">KSPCreate</A>(), <A HREF="../KSP/KSPSetType.html#KSPSetType">KSPSetType</A>(), <A HREF="../KSP/KSPType.html#KSPType">KSPType</A> (for list of available types), <A HREF="../KSP/KSP.html#KSP">KSP</A>, <A HREF="../KSP/KSPNASHSetRadius.html#KSPNASHSetRadius">KSPNASHSetRadius</A>(), <A HREF="../KSP/KSPNASHGetNormD.html#KSPNASHGetNormD">KSPNASHGetNormD</A>(), <A HREF="../KSP/KSPNASHGetObjFcn.html#KSPNASHGetObjFcn">KSPNASHGetObjFcn</A>()
<BR><P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>developer
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/ksp/ksp/impls/cg/nash/nash.c.html#KSPNASH">src/ksp/ksp/impls/cg/nash/nash.c</A>
<BR><A HREF="./index.html">Index of all KSP routines</A>
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