All Questions
3 questions
1
vote
1
answer
234
views
Constrained optimization of sum of squares polynomials
Consider the problem
$$
\min p(x) \text{ subject to } g_j(x)\le 0
\quad
p,g_j\in\text{SOS},
\qquad
(*)
$$
i.e. $p,g_j$ ($j=1,\ldots,m$) are sum of squares (SOS) polynomials. Can this problem be ...
- 710
6
votes
0
answers
255
views
Concavity of a function implicitly defined by a polynomial
Consider the following system of $n$ equations:
\begin{equation}f_j^2 = x_j^2\sum_{i=1}^n A_{ij} f_i
\tag{$\star$}
\end{equation}
where $A_{ij}\geq 0$ are known constants and where $x_j>0$ for ...
- 379
0
votes
1
answer
87
views
Finding maximum of a function with unfixed number of variables
Can anybody solve this:
For a constant positive integer $n\geq6$
find $k$ and positive integers $a_{1},a_{2},...,a_{k}$
that maximize the expression
$$\sum_{i=1}^{k}\left[-4a_{i}^{3}+\left(3n-...
- 396