I'm currently looking at notes on Linear Optimisation and have come across a symbol in the context of formulating a LO problem that looks like this $^{>}{}_<$ but I can't tell what it is supposed to mean. My best guess is that it is supposed to mean $x_j < 0$ or has some relation to the absolute value.
The link to the pdf I'm looking at is: https://ocw.mit.edu/courses/15-093j-optimization-methods-fall-2009/8d61040c41eefd68dda84ce05d82ad71_MIT15_093J_F09_lec02.pdf
Would be grateful for any help with this!
Based on the surrounding context I think it means "$x_j$ could be bigger or smaller than 0"
In the standard form of a LP, the variables are nonnegative (see wikipedia for an example). So this notation is likely chosen to emphasize that these $x_j$ variables (from the set $N_2$, see below image) could be positive or negative.
Then, the document shows how you can use auxiliary variables and add extra constraints in order to turn this into a standard form LP (where all the variables $x_j^+, x_j^-$ are nonnegative).