# Bound on the sum of products

• December 4th 2011, 08:49 AM
robustor
Bound on the sum of products
Let's say that I know that:

$\sum_{i,j} a_{ij} \leq r$, where $0 \leq a_{ij} \leq 0.5$ and $r \geq 0$ and $1 \leq i,j \leq n$

and I also know that

$\sum_{i,j} y_{ij} \leq d$, where $y_{ij} \geq 0$ and $d \geq 0$ and $y$ is zero-diagonal and $1 \leq i,j \leq n$

What do we know about?

$\sum_{i,j} a_{ij} y_{ij} \leq ?$

So far the best I can prove is

$\sum_{i,j} a_{ij} y_{ij} \leq \frac{d}{2}$

Is there a tighter bound?