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Results tagged with nonlinear-optimization
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user 17581
Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.
13
votes
Accepted
An elementary inequality for three complex numbers
I will prove the original inequality.
First, performing the change of variables $x=1/a$, etc., and inverting the harmonic mean, we need
$$
\sum \left|\frac{yz}{x(y+z-x)}\right|\geq \frac32.
$$
Next, …
- 23.7k
3
votes
On a combinatorial inequality
$\def\d{\mathrm{d}}\def\Vol{\mathop{\mathrm{Vol}}}$Okay, this really seems not that straigntforward to generalize the previous answer here. However, here is the method which seems to work (and which s …
- 23.7k
2
votes
Accepted
Why polynomial $\psi^\top(t) A^{-1} \psi(t)$ attains maximum on $[-1, 1]$ at $t = \pm 1$, wh...
It seems that the matrix you present as an example is $A/2$, not $A$; I assume that $A$ is exactly what is defined (so, e.g., $A_{11}=2$, not $1$).
Well, $A$ is the Gram matrix of the basis $\psi$ wi …
- 23.7k
1
vote
Accepted
Detecting linear operator from actions of powers on subspace
An affirmative answer to the first question is easy. Set $V_2=\bigoplus_{i=1}^{n-1} V_1$. Define $A(v,0,0,\dots,0)=(A_1v,v,0,0,\dots)$. Then define the action of $A$ on $0\oplus V_1\oplus 0\oplus\dots …
- 23.7k