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class=MsoPlainText><span style='font-family:"Courier New"'><o:p>&nbsp;</o:p></span></p> <p class=MsoPlainText><span style='font-family:"Courier New"'><span style='mso-spacerun:yes'> </span></span><span style='font-size:12.0pt; font-family:"Times New Roman","serif"'>Optimization involves making a positive definite quantity as small as possible.<span style='mso-spacerun:yes'>  </span><o:p></o:p></span></p> <p class=MsoPlainText><span style='font-family:"Courier New"'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in; margin-left:.75in;margin-bottom:.0001pt;text-indent:-.5in;line-height:normal; mso-list:l0 level1 lfo2;tab-stops:list .75in'><![if !supportLists]><span style='mso-bidi-font-family:Calibri'><span style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><a href="aneal/Aneal.htm">aneal/Aneal.htm</a> The simplest and most desperate method.<span style='mso-spacerun:yes'>  </span>Each location is randomly moved with evan an allowance for some raising.</p> <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in; margin-left:.75in;margin-bottom:.0001pt;text-indent:-.5in;line-height:normal; mso-list:l0 level1 lfo2;tab-stops:list .75in'><![if !supportLists]><span style='mso-bidi-font-family:Calibri'><span style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><a href="amoeba/AMOEBA.htm">amoeba\AMOEBA.htm</a> -- The Nelder Mead algorithim that is the simplest working scheme for the general extremization problem.<span style='mso-spacerun:yes'>  </span>It uses N+1 function values in N dimensions to estimate the best guess for location with a lower value. </p> <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in; margin-left:.75in;margin-bottom:.0001pt;text-indent:-.5in;line-height:normal; mso-list:l0 level1 lfo2;tab-stops:list .75in'><![if !supportLists]><span style='mso-bidi-font-family:Calibri'><span style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><a href="Robmin/Welcome.htm">Robmin\Welcome.htm</a>  An iterative method that utilizes the first and second derivatives of <span style='font-family:Symbol;mso-ascii-font-family:Calibri;mso-hansi-font-family: Calibri;mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>c</span></span><sup>2</sup> along with a multidimensional Marquardt parameter.</p> <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in; margin-left:.75in;margin-bottom:.0001pt;text-indent:-.5in;line-height:normal; mso-list:l0 level1 lfo2;tab-stops:list .75in'><![if !supportLists]><span style='mso-bidi-font-family:Calibri'><span style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><a href="Robmin/PolyPen/Welcome.doc">PolyPen\Welcome.doc</a> <a href="Robmin/PolyPen/Welcome.htm">.htm</a><span style='mso-spacerun:yes'>  </span>Constrained minimization  Lagrange multiplier - Add a Penalty to the quantity being minimized.<span style='mso-spacerun:yes'>  </span>In this case the penalty is designed to keep the denominator of a Pade approximate greater than zero.</p> <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in; margin-left:.75in;margin-bottom:.0001pt;line-height:normal'><o:p>&nbsp;</o:p></p> <p class=MsoNormal style='margin-left:11.25pt'><o:p>&nbsp;</o:p></p> <p class=MsoNormal><o:p>&nbsp;</o:p></p> <p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'><o:p>&nbsp;</o:p></span></p> <p class=MsoPlainText><span style='font-family:"Courier New"'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal><o:p>&nbsp;</o:p></p> </div> </body> </html>