Invalid computation: geo_mean( {mixed real affine/convex} )

Nonconvex
2

I don’t understand the notation, so can’t tell you what to do.

Here is the help for geo_mean.Your argument of ``geo_mean ` clearly violates the rules. have you proven the problem is convex?

help geo_mean

geo_mean Geometric mean.
Y=geo_mean(X), where X is a vector, computes the geometrix mean of X. If any
of the elements of X are negative, then Y=-Inf. Otherwise, it is equivalent
to Y=PROD(X).^(1/LENGTH(X)). All elements must be real.

For matrices, geo_mean(X) is a row vector containing the geometric means of
the columns. For N-D arrays, geo_mean(X) is an array of the geometric means
taken along the first non-singleton dimension of X.

geo_mean(X,DIM) takes the geometric mean along the dimension DIM of X.

geo_mean(X,DIM,W), where W is a vector of nonnegative integers, computes a
weighted geometric mean Y = PROD(X.^W)^(1/SUM(W)). This is more efficient
than replicating the values of X W times. Note that W must be a vector,
even if X is a matrix, and its length must be the same as SIZE(X,DIM).

Disciplined convex programming information:
    geo_mean is concave  and nondecreasing; therefore, when used in CVX
    specifications, its argument must be concave.