GP with change of variables

1

My optimization function looks like this

maximize {x_1^{p_1}}{x_2^{p_2}}....{x_T^{p_T}}

here, x_t are optimization variables and p_t are constants. May be I can express this in GP mode with prod, but GP is still in experimental stage.

Therefore, I want to convert this to log-sum-exp optimization with proper change of variables. How do I do this?

2

CVX is actually performing precisely the log-sum-exp conversion that you are seeking to do, so there is no need for you to do it yourself. But both the GP mode and the log-sum-exp functions rely on CVX’s experimental successive approximation approach.