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6h
comment Why is a Dirac Delta distribution called continuous when it's obviously discrete?
Wikipedia is using the term "continuous" very loosely in that example. They are using it just to mean, like, "defined for all real numbers, as opposed to just defined on the integers". (But even that statement is not really correct, because technically the delta function is a distribution.)
8h
comment Why is a Dirac Delta distribution called continuous when it's obviously discrete?
In what context do people call it continuous?
9h
comment Proving a friend wrong about continuity
Burgundy, if I give you $\epsilon = 1/2$, can you give me $\delta$?
9h
comment Proving a friend wrong about continuity
Just give your friend $\epsilon = 1/2$ and ask them to give you $\delta$.
1d
comment How is an empty set truly “empty”?
While it's true that $\emptyset \subset \emptyset$, this does not imply that $\emptyset \in \emptyset$.
Aug
30
comment Intuitive meaning of “Primal Dual Interior Point Method”
While there are entire books on primal-dual interior point methods, it would definitely be possible for someone here to write an enlightening derivation of a basic primal-dual interior point method that shows the main idea. I hope someone will do that. The section on primal-dual interior point methods in Boyd and Vandenberghe, for example, is fairly short.
Aug
30
comment Intuitive meaning of “Primal Dual Interior Point Method”
It's kind of like solving the KKT conditions by Newton's method. (Except it's a slightly modified version of the KKT conditions.) I think there's a good explanation in the section about primal-dual interior point methods in Boyd and Vandenberghe.
Aug
29
comment Is there a mathematical symbol for “and”?
The second colon is not standard when writing sets. You could express the right hand side as a union of two sets.
Aug
29
comment Is there a mathematical symbol for “and”?
What does the second : mean? What do you mean by "all even numbers, even and odd"?
Aug
29
comment Combinatorial Convex Optimization: Russian paper
You could try scholar.reddit.com.
Aug
28
comment Some clarification on nonlinear PDEs
There must be some mistake in the way you are using Strauss's definition of a linear operator. Can you give more details about that? If $L$ is the operator defined by $L(u) = u_x + u u_y$, it's not necessarily true that $L(u_1 + u_2) = L(u_1) + L(u_2)$, or that $L(c u) = c L(u)$ for all scalars $c$.
Aug
27
comment How do mathematician make sense of “outcome” and “events” in probability?
Have you learned about the axioms for a probability space? You can model physical situations by introducing an appropriate probability space, and then reasoning about the probability space.
Aug
27
comment convex optimization?
But $A$ needs to be a column vector in order for the output of $f$ to be a scalar.
Aug
27
comment What allows us divide/multiply dx in calculus?
@janesmith Note that the function I'm integrating is $ f (g (x)) g'(x) $ , not $ f '(g (x)) g'(x) $, so I think my formula was correct as written.
Aug
26
comment Do I have the correct mental map for adjoint operators for inner product spaces?
I prefer to draw $N(A)$ and $R(A^*)$ as one-dimensional orthogonal subspaces on the left, and draw $R(A)$ and $N(A^*)$ as one-dimensional orthogonal subspaces on the right.
Aug
24
comment How do you find redundant constraints for a feasible region?
Vandenberghe's 236c notes -- specifically the chapter Analytic centering cutting- plane method have some useful material on pruning constraints.
Aug
24
comment Do mathematicians prefer eigenvectors with purely integer entries?
I think the answer is no, there is (usually, at least) no reason to prefer eigenvectors with purely integer entries.
Aug
23
comment Why is it called a “multiset”?
"One of the miseries of life is that everybody names things a little bit wrong, and so it makes everything a little harder to understand." -- Richard Feynman (said at 4:56 in his computer heuristics lecture)
Aug
19
comment proximal operator of weighted L1 norm
Assuming that $\| CX \|_1$ is the sum of the absolute values of $CX$, and that $X \geq 0$ means each component of $X$ is nonnegative, your problem separates into $n$ independent subproblems, one for each column of $X$. So there is no problem with $X$ being a matrix.
Aug
19
comment proximal operator of weighted L1 norm
Since $C X$ is an $m \times n$ matrix, what do you mean by the $1$-norm of $CX$? I suspect you don't mean the matrix norm induced by the vector $1$-norm. Is $\| CX \|_1$ just the sum of the absolute values of the entries of $CX$?