fmincon with a nonlinear constraint would probably work, although because your constraint is non-differentiable, strictly speaking the problem doesn't satisfy fmincon's assumptions. It might be worth doing a preliminary step, where you replace your max constraint with,
for some 
. Then, use that solution as the initial guess when you solve the original problem (which corresponds to
).
. Then, use that solution as the initial guess when you solve the original problem (which corresponds to).
