- M N Problem 2 20 Let Ae 1 Aen Be 1 Ben C Cn Be Some Given Numbers Consider The Following General 1 (45.99 KiB) Viewed 23 times
m n Problem 2. (20%) Let ae,1,..., aen, be,1,..., ben, C₁,..., Cn be some given numbers. Consider the following general Geometric Program: 772 at, 0,2 at, ap₂1. I2 In ΣΠ min TER" l=1 m2 be,2...In ben ses, s.t. Σ 21 Iz l=1 xxx = 1, I1, I2,, In > 0. (a) (5%) Using the transformation y; = log zi (i.e., this is the natural log with log(e) = 1) introduced in the lecture. Rewrite the geometric program in terms of the transformed valuable yi. (b) (15%) Show that the geometric program is equivalent to a convex optimization problem. You may use the fact that the log-sum-exp function: m J(y) = log (exp (de,191 + de,232 + …... - + denyn)) l=1 is convex, for any de,1,..., den, without proving the fact. I1 l=li=1