I don’t know why the error changes when you run cvx_version. You’ll have to wait for someone else to address that.
Do not use binary or integer variables in combination with CVX’s successive approximation method - that combination produces incorrect results, including the possibility of erroneous declaration of the problem being unbounded.
I presume cost_g{4} is >= 0, otherwise your 2nd to last constraint would be non-convex. Given that b is a CVX variable, i don’t see how you can avoid use of CVX’s approximation method (prior to MOSEK 9 with CVX support), except as follows:
Install CVXQUAD https://github.com/hfawzi/cvxquad and the exponential.m replacement for CVX’s version, as discussed at the link. This will invoke CVXQUAD’s Pade Appoximant method and avoid use of CVX’s successive approximation method for certain log and exp related functions (such as entr and rel_entr). But for use of exp as you have, in order for CVXQUAD’s Pade Appoximant method to be invoked instead of CVX’s successive approximation method, I believe you are going to have to re-write the constraint to explicitly use the exponential cone (you can try it first before re-writing, but I think you will have to re-write) using the exponential cone construct
{ x, y, z } == exponential( 1 ) with y = 1,
per mcg;s answer at Solve optimization problems of exp function I don’t know for sure whether the CVXQUAD approach will work correctly when there are binary variables. I have used it only for continuous variable problems and can not test it with binary variables. But I don’t know of any reason why it shouldn’t work correctly. I recommend solving a simple problem first, and then building up to the problem you really want to solve.
I leave you to check that you have done the Big M modeling correctly.