<div dir="ltr">No, no, the constraints only affect the feseable set of the problem. Min or Max depends on the sign of objective function. From mathemtical point of view, the problem is that the KKT conditions are derived for standard formulation (with "less than ..") of NLP.<div><br></div><div>Cheers,<br><div><br></div><div>-gdg<br><div><br></div></div></div></div><div class="gmail_extra"><br><div class="gmail_quote">2017-05-26 0:36 GMT+03:00 David Goldsmith <span dir="ltr"><<a href="mailto:eulergaussriemann@gmail.com" target="_blank">eulergaussriemann@gmail.com</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div>Ah, yes, that convention i am familiar with; maybe to accommodate the "inflexibility" of less numerate potential users (who may be fixated, e.g., on wanting to maximize profit or yield)? Of course, at some point such people may want to minimize something, so hopefully they have someone around to tell them to simply multiply by negative one. ;-)</div><div><br></div><div>DLG</div><div class="HOEnZb"><div class="h5"><div><br><div class="gmail_quote"><div>On Thu, May 25, 2017 at 2:29 PM Kirill Balunov <<a href="mailto:kirillbalunov@gmail.com" target="_blank">kirillbalunov@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div>I'm sorry, perhaps I should more clearly formulate the question. David you are totally right. What I mean by classical: is "less than or equal" type. Of course it's a question of a sign, but still...<div><br></div><div>-gdg</div></div><div class="gmail_extra"><br><div class="gmail_quote">2017-05-26 0:07 GMT+03:00 David Goldsmith <span><<a href="mailto:eulergaussriemann@gmail.com" target="_blank">eulergaussriemann@gmail.com</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div>I would assume that it's because the "or equal to" option allows greater flexibility: if that criterion is allowed by the problem, and the algorithm can find such a solution (e.g., by checking all such corner points), then that's better than not even providing the option, yes? And if you try to "rig" the strict inequality approach by allowing for a little extra room around the corner, then the exact solution might not be found, yes? Indeed, i'm no expert, but i did have a course in this, and IIRC, if your problem allows for equality, then you _must_ separately check all the corners, yes? (In other words, what you state about the "classical formulation" is not what i was taught: I was taught that the specifics of the problem dictate whether any given inequality should be strict or "weak.")</div><div><br></div><div>DLG</div><div><br><div class="gmail_quote"><div><div class="m_8088508145059660051m_-213791253584942538h5"><div>On Thu, May 25, 2017 at 1:49 PM Kirill Balunov <<a href="mailto:kirillbalunov@gmail.com" target="_blank">kirillbalunov@gmail.com</a>> wrote:<br></div></div></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div class="m_8088508145059660051m_-213791253584942538h5"><div><div>Hi,<span class="m_8088508145059660051m_-213791253584942538m_-4622873269180711711m_1794058856554606042m_5887487148427577390gmail-im"><br>I've tried some <code>scipy</code> optimization routines, they work
great!!! But I wondered, why historically for inequality constraints the
type was chosen to be "greater than or equal" type? This is
inconsistent with the classical formulation of non-linear programming
problems.<br><br></span></div><div>Thanks!<br></div><div><br></div>-gdg</div></div></div>
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