Nikos Kazazakis
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$2^1 + 2^2 + \cdots + 2^8$ in binary
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In the binary system (much like in all numbering systems), order has meaning. If you write $0110$ this means $0\times2^3+1\times2^2+1\times2^1+0\times2^0$. Similarly, $11111111$ means $1\times2^7+1\...

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If a convex optimization problem can be NP-Hard, in what sense are convex problems easier than non-convex problems?
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There are special cases of convex problems that can be solved in polynomial time, e.g. a convex QP defined over a simplex. In general, however, convex programming is NP-hard. However, NP-hard by no ...

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if $ b(x) <f(x) \leq g(x)$ where $b, g \in \Theta(x)$ can we state $f(x) \in \Theta(x)?$
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This is much simpler if you use words instead of mathematical stenography: You have two functions, $b$ and $g$, which draw their values from set $\Theta$. You know that the value of $b$ is always ...

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