$$(|y|-x)_{+}^2$$ Is this function with square of positive part of $$|y|-x$$ convex? Also, is it differentiable? If yes, then is it twice differentiable?
I tried plotting epigraph of the function and from the epigraph I think it is convex, but I am not sure about it. Also, I believe this is differentiable for $$|y|-x\geq0\text.$$