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<div id="version" align=right><b>petsc-3.14.5 2021-03-03</b></div>
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<A NAME="KSPQCG"><H1>KSPQCG</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>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_qcg_trustregionradius <r> </B></TD><TD>- Trust Region Radius
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
This is rarely used directly
<P>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
Use preconditioned conjugate gradient to compute
an approximate minimizer of the quadratic function
<P>
q(s) = g^T * s + .5 * s^T * H * s
<P>
subject to the Euclidean norm trust region constraint
<P>
|| D * s || <= delta,
<P>
where
<P>
delta is the trust region radius,
g is the gradient vector, and
H is Hessian matrix,
D is a scaling matrix.
<P>
<A HREF="../KSP/KSPConvergedReason.html#KSPConvergedReason">KSPConvergedReason</A> may be
<pre>
<A HREF="../KSP/KSPConvergedReason.html#KSPConvergedReason">KSP_CONVERGED_CG_NEG_CURVE</A> if convergence is reached along a negative curvature direction,
</pre>
<pre>
<A HREF="../KSP/KSPConvergedReason.html#KSPConvergedReason">KSP_CONVERGED_CG_CONSTRAINED</A> if convergence is reached along a constrained step,
</pre>
<pre>
other <A HREF="../KSP/KSP.html#KSP">KSP</A> converged/diverged reasons
</pre>
<P>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
<H3><FONT COLOR="#CC3333">Currently we allow symmetric preconditioning with the following scaling matrices</FONT></H3>
<A HREF="../PC/PCNONE.html#PCNONE">PCNONE</A>: D = Identity matrix
<A HREF="../PC/PCJACOBI.html#PCJACOBI">PCJACOBI</A>: D = diag [d_1, d_2, ...., d_n], where d_i = sqrt(H[i,i])
<A HREF="../PC/PCICC.html#PCICC">PCICC</A>: D = L^T, implemented with forward and backward solves.
Here L is an incomplete Cholesky factor of H.
<P>
<H3><FONT COLOR="#CC3333">References</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>1. </B></TD><TD>- Trond Steihaug, The Conjugate Gradient Method and Trust Regions in Large Scale Optimization,
SIAM Journal on Numerical Analysis, Vol. 20, No. 3 (Jun., 1983).
</TD></TR></TABLE>
<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/KSPQCGSetTrustRegionRadius.html#KSPQCGSetTrustRegionRadius">KSPQCGSetTrustRegionRadius</A>()
<BR><A HREF="../KSP/KSPQCGGetTrialStepNorm.html#KSPQCGGetTrialStepNorm">KSPQCGGetTrialStepNorm</A>(), <A HREF="../KSP/KSPQCGGetQuadratic.html#KSPQCGGetQuadratic">KSPQCGGetQuadratic</A>()
<P><B></B><H3><FONT COLOR="#CC3333">Level</FONT></H3>developer<BR>
<H3><FONT COLOR="#CC3333">Location</FONT></H3>
</B><A HREF="../../../src/ksp/ksp/impls/qcg/qcg.c.html#KSPQCG">src/ksp/ksp/impls/qcg/qcg.c</A>
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