How can I evaluate the minimum of $$ \left|7x-1\right|+\left|7y-5\right|+\left|7z-1\right| $$ if $x,y,z$ are non negative reals such that $ x+y+z=1$ and $y^2 \le xz$?
Is there a standard way to solve such kind of optimization? I putted here random coefficients which do not satisfy the inequality on the constraint so that the answer shouldn't be trivially zero..