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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="KSPSTCG"><H1>KSPSTCG</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_cg_radius <r> </B></TD><TD>- Trust Region Radius
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
This is rarely used directly
<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>
<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>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
The preconditioner supplied should be symmetric and positive definite.
<P>
<H3><FONT COLOR="#CC3333">References</FONT></H3>
1. Steihaug, T. (1983): The conjugate gradient method and trust regions in large scale optimization. SIAM J. Numer. Anal. 20, 626--637
2. Toint, Ph.L. (1981): Towards an efficient sparsity exploiting Newton method for minimization. In: Duff, I., ed., Sparse Matrices and Their Uses, pp. 57--88. Academic Press
<P>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../KSP/KSPCreate.html#KSPCreate">KSPCreate</A>(), <A HREF="../KSP/KSPCGSetType.html#KSPCGSetType">KSPCGSetType</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/KSPCGSetRadius.html#KSPCGSetRadius">KSPCGSetRadius</A>(), <A HREF="../KSP/KSPCGGetNormD.html#KSPCGGetNormD">KSPCGGetNormD</A>(), <A HREF="../KSP/KSPCGGetObjFcn.html#KSPCGGetObjFcn">KSPCGGetObjFcn</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/ksp/ksp/impls/cg/stcg/stcg.c.html#KSPSTCG">src/ksp/ksp/impls/cg/stcg/stcg.c</A>
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