.. (20%) Let (1,1,...,01,n, 62,1,..., b,n, C1, ..., Cn be some given numbers. Consider the following general Geometric P

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20 Let 1 1 01 N 62 1 B N C1 Cn Be Some Given Numbers Consider The Following General Geometric P 1 (49.46 KiB) Viewed 32 times

.. (20%) Let (1,1,...,01,n, 62,1,..., b,n, C1, ..., Cn be some given numbers. Consider the following general Geometric Program: 21 22 ΣΠ44 m m n 02, 0,1.01.2...In . min ZER Eli=1 I=1 m s.t. ben bu1 62,2...un 11 22 <e, I=1 x;'x72...= 1, 11, 12, ..., ta > 0. (a) Using the transformation Yi = log r; (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. Show that the geometric program is equivalent to a convex optimization problem. You may use the fact that the log-sum-exp function: (b) m f(y) = log (exp (de,191 +d4,242 + ... + de,nyn)) l=1 is convex, for any de,1,..., di,n, without proving the fact.