All Questions
Tagged with combinatorial-optimization real-analysis
7 questions
2
votes
0
answers
70
views
Monotone rearrangements of function, constrained optimization in $\mathcal{L}^p$
By $\mathcal{S}$ let us denote the set of such step functions $f:[0,1]\to [0,1]$ that additionally satisfy:
$$\forall_{ x>\frac{1}{2}} \ \ \lambda\Big(f=x\Big) \ = \ x\cdot \Big[\lambda\Big(f=x\Big)...
user153000
0
votes
1
answer
60
views
Bounding the ratio of the $\ell_1$-norms of two real-valued $n$-vectors as a linear combination of their $n$ element-wise ratios
Let $a_1, a_2, \ldots a_n$ and $b_1, b_2, \ldots b_n$ be two sequences of $n\gg 1$ real numbers such that, for all $1\le i\le n$, we have $0<a_i \le b_i\le 1$. Let the ratio $R$ defined as follows:
...
- 1,677
8
votes
3
answers
296
views
Shrinking subset and product
Given a segment and a value $c$ less than the segment length, let $A_1,\dots,A_n$ be finite unions of intervals on the segment. We choose a finite union of intervals $B$ with $|B|=c$ that maximizes $|...
- 1,209
1
vote
1
answer
117
views
Shrinking subset with disjoint unions
Given a segment and a value $c$ less than the segment length, let $A_1,\dots,A_n$ be disjoint finite unions of intervals on the segment. We choose a finite union of intervals $B$ with $|B|=c$ that ...
- 1,209
4
votes
1
answer
338
views
Minimization of a discrete valued function
$$
\min_{f} \sum_{i=1}^n \max \left( 0, 2f(i) - f(i-1) -f(i+1)\right),
$$
where the minimum is taken over all the functions $f$ from $\{0,1,2,\ldots,n+1\}$ to $[0,x]$, $x <1$, such that $f$ is non-...
user83947
7
votes
2
answers
913
views
Optimal Talmudic Zigzag
I have a finite sequence of positive real numbers $p_1,\dots, p_n$ and I am looking for a monotonically ascending sequence of indices $z_1,\dots, z_k$ that starts with $z_1 = 1$ and ends with $z_k = n$...
1
vote
0
answers
75
views
Characterization of certain families of functions
For $R$ equal $\mathbb{R}$ or $\mathbb{Z}$, let $D^+_R:=\{(x,y)\in R^2\colon x<y\}$. For each natural $n$, let $F_{n,R}$ denote the set of all Borel-measurable functions $f\colon D^+_R\to\mathbb{R}$...
- 128k