I’m trying to solve the following optimization problem.
Minimize M subject to
$0=t_{1,1}\prec t_{1,2}=t_{2,1}\prec t_{1,3}\prec t_{2,2}=t_{3,1}\prec t_{3,2}\prec t_{2,3}\prec t_{3,3}=M$,
$t_{j,k}=a_j x_k+b_j$,
$a_j,b_j,x_k≥0$
where $c\prec d$ means that $d-c\geq1$.
I know that this problem is not convex because of the nonlinear equality constraints. Is there a change of variables that will make this problem convex? If not, what other techniques might be used to solve this problem?