Common operations

• Vector inequality $x \preceq 0$ is the same as max(x) <= 0
  • you can also just broadcast and say x <= 0 and let it figure it out

• element-wise positive or negative component: pos or neg

• PSD: use the psd constraint built into the optimizer

• use hstack to combine different things together

• use inv_pos to take the reciprocal $1/x$, which is convex if $x > 0$.

Other tips

• To optimize only one or a few values in a matrix, I recommend making the whole matrix or vector a varible, and then use equality constraint in the solver

• We are NOT DCP if we have $f(x)\leq 0$ and $g(x)\geq 0$ where $f, g$ are both convex. This is because the standard form requires negating $g$, which turns it into a concave constraint.

• You can’t make numpy arrays with one cp variable, unfortunately.