how can I add 2 log concaves together? without giving me an error : Error using + (line 83)

Disciplined convex programming error:

Illegal operation: {log-concave} + {log-concave}

You can start by verifying you have a convex optimization problem.

Also see the rules for gp at http://cvxr.com/cvx/doc/gp.html#top-level-rules . You can also read Log of sigmoid function (which was already provided in a previous thread).

I contacted the authors of the paper I am working on, and unfortunately, there was no reply. So according to the paper, it says that the problem is convex and as I am using CVX, it gives me the error above. So is there a function that can help me add 2 log-concave expressions together?

There is no such generic function. Perhaps if you provide the full details of the problem, and accessible link to the paper, someone might be able to say something more specific in your case. Does the paper actually say they used CVX, or just that the problem is convex? Please keep in mind the contents of the CVX FAQ link above.

This is the link to the paper. https://arxiv.org/pdf/1908.04082.pdf

I tried to implement equation no.18 using CVX, as they stated in the paper, but the solution was infeasible, so I tried to implement eq.no.14 using CVX and it gave me the above-mentioned error.

The paper does not say that (14) can be solved with CVX. Hence it introduces an approximation to arrive at (18). You solution of (18) was infeasible, so you should follow the advice at https://yalmip.github.io/debugginginfeasible , all of which except for section 1 also applies to CVX. Presumably, the feasibility or infeasibility of the problem depends on the input data. Whether or not the paper’s formulation is any good is between you, your advisor, and the paper’s authors.

## So, I don’t quite understand how CVX work, but can this solution be feasible? `

## Cones | Errors |

Mov/Act | Centering Exp cone Poly cone | Status

--------±--------------------------------±--------

76/ 95 | 8.000e+00 2.039e+01 2.388e-09 | Solved

0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Infeasible

Status: Infeasible`

CVX reported it to be infeasible. But you should follow the advice at 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