Solving this with bnb is a bad idea. The problem is still nonconvex when you relax the integrality constraint (since you have bilinear products). bnb is for problems with convex relaxations.
I would go for a MILP approach. Everything is MILP-representable (nonconvex max, and bilinear product between continuous variable and binary variable)
x*a where x is binary and a is continuous can be handled by replacing the product by a new variable z and adding
[m*(1-x) <= z-a <= (1-x)*M, 0<=z<=M*x
where m and M are suitable chosen big-M constants
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Tutorials.Big-MAndConvexHullsThis conversion from bilinear to MILP is can be done in YALMIP using binmodel. The nonconvex max operations are taken care of automatically, and will lead to more binaries being introduced.
For all operations above, you have to add explicit upper and lower bounds on A.