Problem 4 (Geometric Programming): In this exercise, we discuss a class of nonconvex geometric programs that can be reformulated as convex optimization problems. a) Let a € R" be given with C1 aị = 1....

0. Hint: Substitute the variables r; in an appropriate way and apply the result of part b). d) Use CVX (in MATLAB or Python) to solve problem (1). "/>
Extracted text: Problem 4 (Geometric Programming): In this exercise, we discuss a class of nonconvex geometric programs that can be reformulated as convex optimization problems. a) Let a € R" be given with C1 aị = 1. Show that the matrix A := diag(a) – aaT is positive semidefinite. (Here, diag(a) is a n x n diagonal matrix with a on its diagonal). Hint: The Cauchy-Schwarz inequality rTy < ||r|||||="" x,="" y="" e="" r",="" can="" be="" helpful.="" b)="" we="" define="" f="" :="" r"="" →="" r,="" f(x)="" :="log(E1" exp(x;)).="" show="" that="" f="" is="" a="" convex="" function.="" c)="" convert="" the="" following="" optimization="" problem="" into="" a="" convex="" problem:="" 13="" min-er³="" max="" subject="" to="" rỉ="" +="" 2="">< 2r2="" (1)="" x1,="" 12,="" 13=""> 0. Hint: Substitute the variables r; in an appropriate way and apply the result of part b). d) Use CVX (in MATLAB or Python) to solve problem (1).