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</o:shapelayout></xml><![endif]--></head><body lang=DA link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Thanks Jiadong. I will consider using AMPL instead. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I was just wondering - since DIP supports cutting plane algorithms – as far as I understand – it might also be possible to implement an algorithm using Benders decomposition in a similar way(?). <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Jonas<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal><b><span lang=EN-US style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span lang=EN-US style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> Jiadong Wang <a href="mailto:[mailto:jiadwang@gmail.com]">[mailto:jiadwang@gmail.com]</a> <br><b>Sent:</b> 5. maj 2011 13:32<br><b>To:</b> Jonas Christoffer Villumsen<br><b>Cc:</b> <a href="mailto:dip@list.coin-or.org">dip@list.coin-or.org</a><br><b>Subject:</b> Re: [Dip] Benders decomposition in DIP<o:p></o:p></span></p></div><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal style='margin-bottom:12.0pt'><span lang=EN-US>Hey Jonas<br><br>As far as I know, DIP focuses on Dantzig-Wolfe decomposition. The reason might be that there are some critical applications which can be tailored to column generation methods in OR field.CG is more difficult to implement in terms of transforming between different spaces for the convexification approach.<br><br>Indeed, there are some applications which have many constraints can be more easily solved by Benders decomposition. <br><br>Also convergence issues might be different for these two decompositions. <br><br>there is some example </span><a href="http://www.ampl.com/NEW/LOOP2/index.html"><span lang=EN-US>http://www.ampl.com/NEW/LOOP2/index.html</span></a><span lang=EN-US> showing how to build benders decomposition in AMPL. <br><br>Matt might add more...<br><br>Jiadong<o:p></o:p></span></p><div><p class=MsoNormal><span lang=EN-US>On Thu, May 5, 2011 at 6:44 AM, Jonas Christoffer Villumsen <</span><a href="mailto:jcvi@man.dtu.dk"><span lang=EN-US>jcvi@man.dtu.dk</span></a><span lang=EN-US>> wrote:<o:p></o:p></span></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>Hi all,<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>Is it possible to implement a Benders decomposition approach in DIP? And if so, how would one go about this?<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>If anyone has any experience or ideas for this, I would greatly appreciate your comments. Thanks!<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> <o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>Best regards,<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US>Jonas<o:p></o:p></span></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=EN-US> <span style='color:#888888'><o:p></o:p></span></span></p></div></div><p class=MsoNormal><span lang=EN-US><br>_______________________________________________<br>Dip mailing list<br></span><a href="mailto:Dip@list.coin-or.org"><span lang=EN-US>Dip@list.coin-or.org</span></a><span lang=EN-US><br></span><a href="http://list.coin-or.org/mailman/listinfo/dip" target="_blank"><span lang=EN-US>http://list.coin-or.org/mailman/listinfo/dip</span></a><span lang=EN-US><o:p></o:p></span></p></div><p class=MsoNormal><span lang=EN-US><br><br clear=all><br>-- <br>Jiadong Wang<br>Harold S. Mohler Laboratory<br>Lehigh University<br>200 West Packer Avenue<br>Bethlehem, PA 18015-1582<br><br>Phone No: 484-707-8895<o:p></o:p></span></p></div></body></html>