a*log(1+D/a) can be rewritten as -rel_entr(a,a+D)
I’ll let you deal with the indexing.
If you have access to Mosek, use that as solver, with CVX 2.2. Otherwise, install CVXQUAD’s exponential.m replacement CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions .