tag:blogger.com,1999:blog-593563533834706486.post9207977934830418271..comments2024-03-28T10:35:10.453-04:00Comments on Yet Another Math Programming Consultant: Ill-posed problemErwin Kalvelagenhttp://www.blogger.com/profile/09496091402502236997noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-593563533834706486.post-58653839267293737592013-10-01T03:58:12.344-04:002013-10-01T03:58:12.344-04:00The problem min 1/x, x>=0.0 is ill-posed becau...The problem min 1/x, x>=0.0 is ill-posed because the optimal solution x is +infinity and can never be attained. Another example of an ill-posed problem is one that has nonzero duality gap.<br /><br />In practice MOSEK may say ill posed for other reasons. A very bad scaling could cause the message for instance. Or if you extremely large bounds or penalty values in the objective. Another reason is that the problem may not convex even though the user thinks it is.<br /><br />It is impossible for MOSEK to be precise about what is causing the ill-posedness because there is no single reason causing it. <br />Ignoring the message and moving to another optimizer may of course be a fix that solves the issue. The other optimizer may presolve and scale the problem differently and hence be lucky to work around the issue. Of course I can not exclude MOSEK is doing something stupid that the other optimizer does not. <br /><br />An alternative route is to provide the problem to MOSEK support for an investigation. Frequently that leads to pinpointing an unfortunate model model formulation.<br /><br />Btw the characteristic of an ill-posed problem is a tiny perturbation in the data changes the solution dramatically. This should make it obvious that is very hard to deal with such problems. Note the problem min 1/x, x>=1.0e-10 is not ill-posed.<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Erling D. Andersenhttps://www.blogger.com/profile/12871077105817644633noreply@blogger.com