Hello, everyone! Thank you for your attention !

I have one problem about this expression, how to express it by CVX?

**Variable** **:** tao[n] , l1[n] and l2[n]

help log_sum_exp

log_sum_exp log(sum(exp(x))).

log_sum_exp(X) = LOG(SUM(EXP(X)).`When used in a CVX model, log_sum_exp(X) causes CVX's successive approximation method to be invoked, producing results exact to within the tolerance of the solver. This is in contrast to LOGSUMEXP_SDP, which uses a single SDP-representable global approximation. If X is a matrix, LOGSUMEXP_SDP(X) will perform its computations along each column of X. If X is an N-D array, LOGSUMEXP_SDP(X) will perform its computations along the first dimension of size other than 1. LOGSUMEXP_SDP(X,DIM) will perform its computations along dimension DIM. Disciplined convex programming information: log_sum_exp(X) is convex and nondecreasing in X; therefore, X must be convex (or affine).`

You will need to divide by `log(2)`

because `log_sum_exp`

is based on `log`

, not `log2`

.

Despite what the help says, CVX’s Successive Approximation method is not used if CVX 2.2+Mosek9.x or 10.x are used (preferred), or if CVXQUAD’s `exponential.m`

replacement is used (2nd choice to use of CVX 2.2 + Mosek 9.x or 10.x)

Thank you for your reply very much!

According to your suggestion, I transform the constraint as follows:

X=[ ln(sigma/P[n])， 2log(A)+l1(n)， 2log（C)+l2(n) ]

tao(n)*log(2) >= log(P(n)/sigma) +log_sum_exp(X);

I think you got it right, except in the first element of `X`

, you forgot to square `sigma`

, or multiply the log by 2, And of course the `ln`

in that element should be `log`

.

Yes, thank you for your reminder. Thank you very much !