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2 votes
1 answer
107 views

Does this simple non-convex problem involving discrete phase shifts have an exact solution?

Let the optimization problem be \begin{equation} \max_{\phi_n} \left|\sum_{n=1}^N e^{i\phi_n} a_n \right|, \end{equation} where $a_n\in\mathbb{C}$ and the optimization variables have discrete phase ...
1 vote
0 answers
131 views

Lower bound on the value $\textbf{1}^Tx$ such as $Ax\geq b$

The problem may be formulated as follows: We are given a set of $m$ positive numbers $\{b_1,...,b_m\}$ and a set of $n$ positive numbers $\{v_1,...,v_n\}$. We have $v_j\leq K$, $j=1,...,n$, for a ...