<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:12.0pt;
font-family:"Calibri",sans-serif;}
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
{mso-style-priority:34;
margin-top:0in;
margin-right:0in;
margin-bottom:0in;
margin-left:.5in;
font-size:12.0pt;
font-family:"Calibri",sans-serif;}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:12.0pt;
font-family:"Calibri",sans-serif;}
.MsoPapDefault
{mso-style-type:export-only;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
/* List Definitions */
@list l0
{mso-list-id:1268391808;
mso-list-type:hybrid;
mso-list-template-ids:-1911913020 67698705 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
@list l0:level1
{mso-level-text:"%1\)";
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level2
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level3
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
@list l0:level4
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level5
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level6
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
@list l0:level7
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level8
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level9
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
ol
{margin-bottom:0in;}
ul
{margin-bottom:0in;}
--></style>
</head>
<body lang="EN-US" link="#0563C1" vlink="#954F72" style="word-wrap:break-word">
<div class="WordSection1">
<p class="MsoNormal"><span style="font-size:11.0pt">Hello,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">I’ve been using the default newton line search nonlinear solver in petsc. I recently discovered that the default line search method is bt – backtracking. I have two questions.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<ol style="margin-top:0in" start="1" type="1">
<li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1"><span style="font-size:11.0pt">How exactly does the backtracking line search use the L2 norm of the function to modify the newton step? What is the formula?<o:p></o:p></span></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo1"><span style="font-size:11.0pt">Why is backtracking default? I would think that the basic method, which is a standard Newton method, would be default.<o:p></o:p></span></li></ol>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">-Justin<o:p></o:p></span></p>
</div>
</body>
</html>