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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML3.2 EN">
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<TITLE>TAONTR</TITLE>
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<BODY BGCOLOR="FFFFFF">
   <div id="version" align=right><b>petsc-3.7.5 2017-01-01</b></div>
   <div id="bugreport" align=right><a href="mailto:petsc-maint@mcs.anl.gov?subject=Typo or Error in Documentation &body=Please describe the typo or error in the documentation: petsc-3.7.5 v3.7.5 docs/manualpages/Tao/TAONTR.html "><small>Report Typos and Errors</small></a></div>
<A NAME="TAONTR"><H1>TAONTR</H1></A>
Newton's method with trust region for unconstrained minimization. At each iteration, the Newton trust region method solves the system. NTR expects a <A HREF="../KSP/KSP.html#KSP">KSP</A> solver with a trust region radius. min_d  .5 dT Hk d + gkT d,  s.t.   ||d|| &lt; Delta_k 
<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>-tao_ntr_ksp_type </B></TD><TD>- "nash","stcg","gltr"
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_pc_type </B></TD><TD>- "none","ahess","bfgs","petsc"
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_bfgs_scale_type </B></TD><TD>- type of scaling with bfgs pc, "ahess" or "bfgs"
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_init_type </B></TD><TD>- "constant","direction","interpolation"
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_update_type </B></TD><TD>- "reduction","interpolation"
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_min_radius </B></TD><TD>- lower bound on trust region radius
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_max_radius </B></TD><TD>- upper bound on trust region radius
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_epsilon </B></TD><TD>- tolerance for accepting actual / predicted reduction
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_mu1_i </B></TD><TD>- mu1 interpolation init factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_mu2_i </B></TD><TD>- mu2 interpolation init factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_gamma1_i </B></TD><TD>- gamma1 interpolation init factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_gamma2_i </B></TD><TD>- gamma2 interpolation init factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_gamma3_i </B></TD><TD>- gamma3 interpolation init factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_gamma4_i </B></TD><TD>- gamma4 interpolation init factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_theta_i </B></TD><TD>- thetha1 interpolation init factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_eta1 </B></TD><TD>- eta1 reduction update factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_eta2 </B></TD><TD>- eta2 reduction update factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_eta3 </B></TD><TD>- eta3 reduction update factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_eta4 </B></TD><TD>- eta4 reduction update factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_alpha1 </B></TD><TD>- alpha1 reduction update factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_alpha2 </B></TD><TD>- alpha2 reduction update factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_alpha3 </B></TD><TD>- alpha3 reduction update factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_alpha4 </B></TD><TD>- alpha4 reduction update factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_alpha4 </B></TD><TD>- alpha4 reduction update factor
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_mu1 </B></TD><TD>- mu1 interpolation update
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_mu2 </B></TD><TD>- mu2 interpolation update
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_gamma1 </B></TD><TD>- gamma1 interpolcation update
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_gamma2 </B></TD><TD>- gamma2 interpolcation update
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_gamma3 </B></TD><TD>- gamma3 interpolcation update
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_gamma4 </B></TD><TD>- gamma4 interpolation update
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-tao_ntr_theta </B></TD><TD>- theta interpolation update
</TD></TR></TABLE>
<P>

<P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>beginner
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/tao/unconstrained/impls/ntr/ntr.c.html#TAONTR">src/tao/unconstrained/impls/ntr/ntr.c</A>
<BR><A HREF="./index.html">Index of all Tao routines</A>
<BR><A HREF="../../index.html">Table of Contents for all manual pages</A>
<BR><A HREF="../singleindex.html">Index of all manual pages</A>
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