My approach to this is to solve it numerically.
Given N strategies S1, S2, ..., SN, solve for this:
OG = MAX(w1 * LN(R1) + w2 * LN(R2) + ... + wN * LN(RN))
where
OG is the optimal rate of growth
R1, R2, ..., RN are the returns of strategies S1, S2, ..., SN
w1, w2, ..., wN are the weights...