I have the following optimization problem: \begin{equation} \begin{aligned} \underset{x}{\text{min}} {\sum_{i=1}^{k}} w_{i}x \end{aligned} \end{equation}
Is the solution x = 0? Here $w_{i}$ is given. Both $w_{i}$ and x are scalars.
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1No, there is no minimum. – Alex Silva Nov 23 '18 at 12:41
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Hint, select $x_i = -t w_i$ and see what happens when you let $t$ tend to $\infty$ – Johan Löfberg Nov 23 '18 at 16:17