The following unconstrained optimization problem is strictly and jointly concave in all its decision variables (q’s):
max sum_i (u_i/b_i).* q_i - (1 - sum_i ((1/b_i)* q_i)) .* log(1 - sum_j (q_j)) + log(1 - sum_j (q_j)) - sum_i (entr(q_i)./b_i)
All u_i, b_i are scalars.
q is a 1xd vector and the indices i & j represents two different q’s but when we sum over i or j basically we’re summing over the same q vector of d dimension.
The objective function has 4 terms, all are acceptable by CVX except for the second term [(1 - sum_i ((1/b_i)* q_i)) .* log(1 - sum_j (q_j))] is not due to DCP rule.
I’d appreciate any suggestion on how to handle this term to make it acceptable by CVX.