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1d
comment Turn off the ovens! An optimization problem
How well do Baron and Couenne scale on larger problems? Are there guarantees on finding the global minimum? (I presume the answers to both these questions can't be favourable.)
1d
comment Conditions for convex hulls
Given a finite set of points in an affine space, their convex hull always exists.
1d
comment convex optimization with multiple nonsmooth terms
Minimize $\underbrace{f(x)}_{\text{first function}}+\underbrace{g(z_1)+h(z_2)}_{\text{second function}}$ subject to $\begin{bmatrix}x\\x\end{bmatrix}=\begin{bmatrix}z_1\\z_2\end{bmatrix}$.
2d
comment convex optimization with multiple nonsmooth terms
ADMM will work.
2d
comment What is $\left | \left | A \right | \right |$ equals to in linear algebra?
Um, what are you trying to say with your comments?
Feb
10
comment Explain “homotopy” to me
@Asaf: I think it becomes a neat distillation of the StackExchange model -- in appearance we explain things to "the asker", but really we explain them to all the other people who might read our answers in the future.
Feb
10
comment What's the equation for a rectircle? (Perfect rounded-corner rectangle without stretching on only one dim)
Surely you already know what a rounded rectangle looks like.
Feb
9
comment Can covariance (X,Y) be easily expressed in term of Var(X), Var(Y), E(X), and E(Y)?
Consider (i) $X$ and $Y$ are i.i.d. standard normal, (ii) $X$ is standard normal and $Y=X$. Both cases have the same $E(X)$, $E(Y)$, $\operatorname{Var}(X)$, $\operatorname{Var}(Y)$ but different $\operatorname{Cov}(X,Y)$.
Feb
8
comment A connectivity-preserving function from a connected set onto an interval
I believe it would be useful to think of $f$ not as a projection to an interval, but as a scalar field over $C$ all of whose level sets are connected. For example, the global minimum and global maximum must be attained over connected sets, and there should be no other critical points.
Feb
8
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
Feb
7
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.
Feb
7
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.
Feb
7
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.
Feb
6
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
Feb
5
comment Continuity of Parameterized Optimal Solution
Is $f$ continuous in $y$?
Feb
5
comment Approximating the number $e$ through computer simulation - mathematical background
@Ian Oops, I was looking at an old version of the question.
Feb
5
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.