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4h
comment What do people mean by “finding the end of $\pi$”
More formulas than you can shake a stick at: en.wikipedia.org/wiki/Approximations_of_%CF%80
7h
comment Given $5$ points on a sphere, divide the surface into $5$ congruent connected regions containing one point.
Sure. Pick an axis along which all of the points have distinct projections, then define the regions to look something like this.
15h
comment Understanding ADMM: how is it applied to this particular problem?
Yes but the optimality conditions as stated in the Boyd et al. paper only apply when the domain is $\mathbb R^n$. What you are trying to do is like minimizing $f(x)=x$ over $x\in[-1,1]$ and being surprised that the unconstrained optimality condition $f'(x)=0$ is unsatisfiable.
16h
comment Understanding ADMM: how is it applied to this particular problem?
I would formulate your problem as minimizing $f(u) + g(v)$ subject to $Au+Bv=0$ as you have above, but with $f(x_1,x_2) = \langle\text{your original objective}\rangle + \chi_{\mathcal X_1}(x_1,x_2)$ and $g(y,z) = \chi_{\mathcal Y}(y) + \chi_{\mathcal Z}(z)$. Here $\chi_{\mathcal A}$ is the indicator function of the set $\mathcal A$, i.e. $0$ inside and $\infty$ outside.
2d
comment Does a convex hull solution in 3 dimensions result in a minimum-area or maximum-volume solution?
Relevant previous question: Convex Hulls vs Shrink Wrap
2d
comment Continuity of Parameterized Optimal Solution
Is $f$ continuous in $y$?
2d
comment Approximating the number $e$ through computer simulation - mathematical background
@Ian Oops, I was looking at an old version of the question.
2d
comment Is there a name for dividing a set into pieces, some of which may be empty?
Something about equivalence classes induced by equality under $\operatorname{sgn}\circ f$?
Feb
4
comment Is there anything wrong with this definition of discontinuity?
That's a discontinuous function, of course, the problem is that it doesn't satisfy your definition of discontinuity. That is, it fails to be discontinuous under your definition.
Feb
4
comment Is there anything wrong with this definition of discontinuity?
Two problems: (i) you need "for all $x\ne c$" or your definition is never satisfied, and (ii) a function continuous only on one side still fails to satisfy your definition.
Feb
4
comment Is there anything wrong with this definition of discontinuity?
This is actually a definition of not being locally constant.
Feb
4
comment In graph theory, what would a negative number of vertices mean?
Before you even start talking about graphs you have to decide what it means for a set to have a negative number of elements. Maybe start here.
Feb
4
comment Is there no (basic) math webfont?
But when writing sin x you want "$\sin x$", not "$sin\ x$". You get italicized variables not by using a font whose letters are always in italics, but by explicitly switching to an italic font when typesetting variables.
Feb
4
comment What is a “box” in this context “let $B ⊂ R^n$ be a box that can be partitioned into boxes”?
By "an integer length side" I think they mean "a side of integer length". That is, at least one of $(b_1,b_2,\ldots,b_n)$ is an integer.
Feb
3
comment Why do people prefer cosine to sine when speaking of harmonic oscillation?
If you have a consistent delay between observing the zero crossing and pressing the button, it will still cancel out when taking the difference between the two times. :)
Feb
3
comment What non-convex functions be written as the $\min$ of multiple convex functions?
Only if your function is piecewise convex with a finite number of pieces.
Feb
3
comment Does a mapping from one metric space to another metric space preserve star-likeness of regions?
Is the metric compatible with the vector space structure? That is, is $d(ax_1,ax_2)=ad(x_1,x_2)$, and $d(x_1+y,x_2+y)=d(x_1,x_2)$?
Feb
3
comment What non-convex functions be written as the $\min$ of multiple convex functions?
Assuming gerw means the characteristic function, $i_{\{x'\}}(x)$ is convex and $f(x')$ is constant.
Feb
3
comment An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all?
But see this previous answer by mike4ty4.
Feb
3
comment An obvious pattern to $i\uparrow\uparrow n$ that is eluding us all?
So your sequence is $i\uparrow\uparrow n$, also written as ${}^ni$, and you're looking for a "smooth" extension to real heights ${}^xi$. Wikipedia has some discussion about it, though it begins with the statement that "At this time there is no commonly accepted solution to the general problem of extending tetration to the real or complex values of $n$."