<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">You have a non-concave maximization problem with three stationarity points, and you're starting the solver on one of them. Being a local solver, all things being equal, it'll naturally converge on the closest point that satisfies optimality conditions. If you had started from x := 0.4999, you'd get a different answer.<div><div><span class="Apple-tab-span" style="white-space:pre"> </span>F = 1</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>x = 0.146447</div></div><div><br></div><div>Also, your problem has non-unique global optima, so depending on where your initial guess is, you'll end up on one or the other. </div><div><br></div><div>Dave</div><div><br><div><blockquote type="cite"><br><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 0.5);"><b>From: </b></span><span style="font-family:'Helvetica'; font-size:medium;">Paul Smith <<a href="mailto:phhs80@gmail.com">phhs80@gmail.com</a>><br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 0.5);"><b>Date: </b></span><span style="font-family:'Helvetica'; font-size:medium;">June 17, 2010 11:39:39 AM GMT-04:00<br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 0.5);"><b>To: </b></span><span style="font-family:'Helvetica'; font-size:medium;">ipopt mailing list <<a href="mailto:ipopt@list.coin-or.org">ipopt@list.coin-or.org</a>><br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 0.5);"><b>Subject: </b></span><span style="font-family:'Helvetica'; font-size:medium;"><b>[Ipopt] A maximization problem returns a minimum</b><br></span></div><br><br>Dear All,<br><br>I am running this simple model through AMPL and Ipopt 3.8.0:<br><br>--------------------------------------<br>var x >= 0;<br><br>let x := 0.5;<br><br>maximize F:<span class="Apple-tab-span" style="white-space:pre"> </span><br> -16 * x * (x-1) * (2*x - 1)^2;<br><br>subject to R1:<br> x <= 1;<br>--------------------------------------<br><br>Ipopt returns the following solution:<br><br>«EXIT: Optimal Solution Found.<br><br>Ipopt 3.8.0: Optimal Solution Found<br><br>suffix ipopt_zU_out OUT;<br>suffix ipopt_zL_out OUT;<br>ampl: display F, x;<br>F = 0<br>x = 0.5».<br><br>However the returned solution is a minimum and NOT a maximum. What am<br>I not understanding?<br><br>Thanks in advance,<br><br>Paul<br><br></blockquote></div><br></div></body></html>