Enthusiastic CS major interested in Optimization Theory here. Pardon me for overlooking something obvious.
I'm referring to this nice tutorial/ebook: http://faculty.uml.edu/cbyrne/optfirst0.pdf
In this, I'm specifically looking at Chapter 3, Section 3.3 (pages 26, 27). I understand the part till where the author applies GAGM (Generalized Arithmetic-Geometric Mean Inequality) to the posynomial. However, I did not understand the reduction from step (3.6) to (3.7). Can anyone help explaining this?
Thanks for reading!
The statement $(3\cdot 7)$ says: $$g(t)\geq \prod_{j=1}^m\left(\frac{u_j(t)}{\delta_j}\right)^{\delta_j}\tag{3.6}$$
And we know that from $(3\cdot 3)$ in the book: $$u_j(t)=c_i\prod_{i=1}^{n}t_i^{a_i,j} \tag{3.3}$$
if we replace $(3.3)$ in $(3.6)$ we obtain: $$g(t)\geq \prod_{j=1}^m\left(\frac{u_j(t)}{\delta_j}\right)^{\delta_j}= \prod_{j=1}^m\left(\frac{c_i\prod_{i=1}^{n}t_i^{a_i,j} }{\delta_j}\right)^{\delta_j}=\prod_{j=1}^m\left(\frac{c_j}{\delta_j}\right)^{\delta_j}\left(\prod_{j=1}^m\prod_{i=1}^nt_i^{a_{i,j}\delta_j}\right)$$
which gives you $(3.7)$