I would like to ask a question about the convexity of the constraint functions.
We have constraints for an optimization problem:
$$x=x^+-x^-$$ $$y=y^+-y^-$$ $$x^+\geqslant A(y^+)^2$$ $$x^-\geqslant A(y^-)^2$$ $$(xx^+)^{0.5}\geqslant0$$ $$(-xx^-)^{0.5}\geqslant0$$
where $x,y$ are variables, $x^+,x^-,y^+,y^-$ are positive variables, and $A$ is a positive constant.
Are the constraint functions convex?
Thank you.
Dylan