I think you should try to solve these subproblems with the primal simplex algorithm. It would most likely do minimizing sum of infeasibility and will likely be less degenerated. Actually this is equal to a old strategy by the great GDB himself, where he suggest minimizing primal sum of infeasibility on the subset of dual degenerated variables (in this case all of them).<br>
You are right that all the duals in theory are zero in dual simplex in this case, but in practice they contain small perturbations to avoid the degeneracy issue, so depending on the solver it may or may not exploit this. <br>
<br><div class="gmail_quote">On Mon, Jun 29, 2009 at 7:55 PM, Bulutoglu Dursun A Civ AFIT/ENC <span dir="ltr"><<a href="mailto:Dursun.Bulutoglu@afit.edu">Dursun.Bulutoglu@afit.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
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<p dir="ltr"><span lang="en-us"><font face="Calibri">Dear Clp forum,</font></span></p>
<p dir="ltr"><span lang="en-us"><font face="Calibri">I am using an IP solver that uses Clp-1.7.</font></span><span lang="en-us"> <font face="Calibri">My IP problems are</font></span><span lang="en-us"> <font face="Calibri">all</font></span><span lang="en-us"> <font face="Calibri">feasibility problems.</font></span></p>
<p dir="ltr"><span lang="en-us"><font face="Calibri">I am trying to find all feasible solutions to an IP.</font></span><span lang="en-us"> <font face="Calibri">I am using the zero function as my objective (</font></span><span lang="en-us"><font face="Calibri">i.e.</font></span><span lang="en-us"> <font face="Calibri">all of my objective function</font></span><span lang="en-us"><font face="Calibri">'</font></span><span lang="en-us"><font face="Calibri">s</font></span><span lang="en-us"><font face="Calibri"> coefficients</font></span><span lang="en-us"><font face="Calibri"> are equal to zero).</font></span><span lang="en-us"><font face="Calibri"></font></span><span lang="en-us"> <font face="Calibri">Then i</font></span><span lang="en-us"><font face="Calibri">n the dual simplex algorithm</font></span><span lang="en-us"><font face="Calibri"> all the calculations involving reduced costs are</font></span><span lang="en-us"> <font face="Calibri">unnecessary. Skipping these calculations will</font></span><span lang="en-us"> <font face="Calibri">undoubtedly speed up the dual simplex</font></span><span lang="en-us"> <font face="Calibri">calculations in solving an LP relaxation within an IP.</font></span><span lang="en-us"><font face="Calibri"></font></span><span lang="en-us"> </span></p>
<p dir="ltr"><span lang="en-us"><font face="Calibri">I was wondering if there is a version of Clp whose dual simplex componen</font></span><span lang="en-us"><font face="Calibri">t</font></span><span lang="en-us"><font face="Calibri"> skips</font></span><span lang="en-us"> <font face="Calibri">calculations involving reduced costs</font></span><span lang="en-us"><font face="Calibri"> when the objective function is the zero function</font></span><span lang="en-us"><font face="Calibri">.</font></span><span lang="en-us"><font face="Calibri"></font></span><span lang="en-us"> </span></p>
<p dir="ltr"><span lang="en-us"><font face="Calibri">Dursun Bulutoglu</font></span><span lang="en-us"></span></p>
<p dir="ltr"><span lang="en-us"></span></p>
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