<p dir="ltr">Oops, you beat me to it. Just adding one thing, since I know Brad is the author of an excellent AD tool...</p>
<p dir="ltr">Keep in mind that you can always calculate the simple bounds multipliers yourself after IPOPT finishes. It follows easily from the KKT conditions. All you need is a reverse mode sweep on the Lagrangian function.</p>
<p dir="ltr">Joel</p>
<div class="gmail_quote">On Jul 20, 2015 12:18 AM, "Tony Kelman" <<a href="mailto:kelman@berkeley.edu">kelman@berkeley.edu</a>> wrote:<br type="attribution"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">This may change depending on the setting of the option fixed_variable_treatment <a href="http://www.coin-or.org/Ipopt/documentation/node43.html#SECTION000114060000000000000" rel="noreferrer" target="_blank">http://www.coin-or.org/Ipopt/documentation/node43.html#SECTION000114060000000000000</a><br>
<br>
"For both "make_constraints" and "relax_bounds", bound multipliers are computed for the fixed variables."<br>
<br>
<br>
-----Original Message----- From: Brad Bell<br>
Sent: Sunday, July 19, 2015 3:01 PM<br>
To: <a href="mailto:ipopt@list.coin-or.org" target="_blank">ipopt@list.coin-or.org</a><br>
Subject: [Ipopt] finalize solution<br>
<br>
Consider the case where the lower limit and upper limit is equal for one<br>
of the primal variable components; e.g.,<br>
x_l[j] = x_u[j]<br>
in the get_bounds_info function.<br>
<br>
I appears that in this case, finalize_solution will have<br>
z_L[j] = z_U[j] = 0.<br>
Is this how Ipopt works ?<br>
<br>
If so, consider the optimization problem<br>
minimize x[0]^2 subject to 1 <= x[0] <= 1<br>
In this case, it appears to me, that the final multiplier z_L[0], in<br>
finalize_solution, should be non-zero.<br>
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</blockquote></div>