Timeline for When does $\min_x \max_yf(x,y) = \min_y \max_x f(x,y)$ hold for a real function $f(x,y)$?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 27, 2020 at 9:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 28, 2020 at 8:35 | comment | added | valle | @YaakovBaruch The domains of $x,y$ are $\mathbb R^n$ (with different dimensions possibly). In my current application they are unbounded. | |
| S Mar 28, 2020 at 8:23 | history | suggested | VS. | CC BY-SA 4.0 |
Elaborated title
|
| Mar 28, 2020 at 7:02 | review | Suggested edits | |||
| S Mar 28, 2020 at 8:23 | |||||
| Mar 26, 2020 at 16:48 | comment | added | Yaakov Baruch | Also, what are the domains for $x$ and $y$ that you are most interested in? | |
| Mar 26, 2020 at 16:46 | comment | added | Yaakov Baruch | Well, I would maybe consider in this case editing some of the rationale into the question itself. I think it deserves more visibility than it has received so far, perhaps due to it being misunderstood as some sort of playing around with Minimax variants? | |
| Mar 26, 2020 at 14:04 | history | edited | valle | CC BY-SA 4.0 |
added 203 characters in body
|
| Mar 26, 2020 at 14:03 | comment | added | valle | In your example $ax+by$, the saddle occurs at the boundary of the domain, where the gradient of $f$ need not be zero. I do not expect my equality to hold in that case. | |
| Mar 26, 2020 at 14:01 | comment | added | valle | @YaakovBaruch I have a variational formulation of a certain statistical mechanics problem, where I derive an optimization like one side of this equation, but where it would make a lot of sense physically that the optimization were like the other side. I need to understand when both sides are equal, because if they are not it would be potentially interesting. Numerically I find they typically are equal (but this could be because I am only looking at the points where the derivative are zero). | |
| Mar 26, 2020 at 12:59 | comment | added | Yaakov Baruch | It's a slightly strange question, since for example the equality wouldn't even hold for $ax+by$ in $[0,1]\times [0,1]$ (unlike the Minimax Theorem). Any particular reason why you are interested in this? | |
| Mar 25, 2020 at 9:56 | history | edited | valle | CC BY-SA 4.0 |
edited title
|
| Mar 24, 2020 at 19:39 | comment | added | valle | Why the close vote? | |
| Mar 24, 2020 at 19:38 | answer | added | valle | timeline score: 1 | |
| Mar 24, 2020 at 17:00 | review | Close votes | |||
| Mar 25, 2020 at 10:55 | |||||
| Mar 24, 2020 at 13:35 | comment | added | valle | Also posted here: math.stackexchange.com/q/3592868/10063 | |
| Mar 24, 2020 at 13:35 | history | asked | valle | CC BY-SA 4.0 |