Disciplined convex programming error: Invalid operation: * {positive concave matrix}

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As i suggested before, try using Mosek. Do not use the quiet option, and pay attention to any warnings.

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I was not able to reformulate the problem from the link(5 Exponential cone optimization — MOSEK Modeling Cookbook 3.3.0) which you have provided, can we reformulate 1/alpha1 using taylor series and make that expression affine?

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Did you try using
log2(1-lambda/alpha1) can be reformulated as
log(1-lambda*inv_pos(alpha1))/log(2)
with Mosek as solver as I suggested in a previous post? That is easier to do in CVX than the Mosek Modeling Cookbook formulation, which does not utilize CVX’s built-in capabilities, and therefore requires lower-level (more complicated) formulation than needed in CVX for this expression.

I have a lot of difficulty determining what the problem specification and formulation are for your various posts.