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Results tagged with nonlinear-optimization
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user 36721
Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.
4
votes
0
answers
116
views
An inequality for three iid random variables with a log-concave density
It was previously shown that
$$H\ge cG,\tag{1}$$
where $c:=1/14334$,
$$G:=E|X-Y|,\quad H:=E|X-Y|-\tfrac12\,E|X+Y-2Z|,$$
and $X,Y,Z$ are independent random variables with the same log-concave density.
…
- 111k
2
votes
0
answers
60
views
Minimizing a certain norm of the identity operator on $\mathbb R^2$
$\newcommand\R{\mathbb R}\newcommand\Q{\mathcal Q}$For mutually orthogonal vectors unit vectors $a=[a_1,\dots,a_n]^T$ and $b=[b_1,\dots,b_n]^T$ in $\R^n=\R^{n\times1}$ (so that $n\ge2$) and for all $x …
- 111k
5
votes
1
answer
295
views
On a certain norm of the identity operator on $\mathbb R^2$
$\newcommand\R{\mathbb R}\newcommand\Q{\mathcal Q}$For mutually orthogonal vectors unit vectors $a=[a_1,\dots,a_n]^T$ and $b=[b_1,\dots,b_n]^T$ in $\R^n=\R^{n\times1}$ (so that $n\ge2$) and for all $x …
- 111k
7
votes
1
answer
336
views
An elementary inequality for three complex numbers
The following problem arose in asymptotic analysis of difference equations.
Numerical maximization suggests that for all nonzero complex numbers $a,b,c$ we have
$$h\big(r(a,b,c),r(b,c,a),r(c,a,b)\big …
- 111k
1
vote
0
answers
50
views
Sum of squared nearest-neighbor distances between points on the sides of a rectangle
For positive real numbers $a,b$, let $R$ denote the $a\times b$ rectangle $[0,a]\times[0,b]$. Let $A_1,\dots,A_4$ be points on the sides of $R$, one point on each side. For each $j=1,\dots,4$, let $s_ …
- 111k
2
votes
1
answer
128
views
Optimal-score partitions
The question about throwing darts asked on the MathOverflow page Sacred Geometry of Chance was not well received, apparently because of "[t]oo much noise around the actual math", as stated in a well-r …
- 111k
6
votes
1
answer
527
views
Bound on the sum of arguments
Problem: Show that for all real $s,t,u$ and all complex $z$ with $|z|<1$ one has
$$(*)\qquad \arg\frac{1-zf(s-u)}{1-zf(s+u)}
+\arg\frac{1-zf(t+u)}{1-zf(t-u)}<\pi,
$$
where $f$ is the characteristic …
- 111k