Minimize the distance from $(x_0, y_0)$ in the 4th quadrant to the curve $y = |x|$
I know that the minimization problem is:
minimize $$f(x,y)= (x-x_0)^2 + (y-y_0)^2$$ subject to$$ g(x,y) = y - |x|= 0 $$
Since the constraint g(x,y) is not differentiable, how can I use two inequality constraints to solve this problem?