Can you explain to me the equation 2.54 on page 48 of this online book:
$$ \boldsymbol{c}^* = argmin_c \space ||\boldsymbol{x}-g(\boldsymbol{c})||_2 $$
- What does the asterisk in $\boldsymbol{c}^*$ mean?
- Wikipedia says that $arg$ is "a function operating on complex numbers". That isn't the case in this context, is it? So what do $arg$, $min$, $argmin$ (and $max$ and $argmax$ for that matter) mean, and how do they differ?
This is a common way of expressing things in optimization problems.
If I write $$ y = \text{argmin}_x \,f(x) $$ it means that $y$ is the value of $x$ that makes $f(x)$ a minimum. In other words, $y$ is the function argument that produces the minimum value.
The asterisk doesn't mean anything. The author just chose to use the symbol $c*$ to denote the argument giving the minimum value.
This is not related to the use of "arg" with complex numbers, which is what you found in Wikipedia.