Question

For each of the following optimization problems (a) check if problem is convex, (b) write a CVX code that solves it, and (c) write down the optimal solution by running CVX.

(a) Minimize ||Ax – 6112 [1 2] 3 4 and b= with A= 8 5 6
(b) Minimize z = V2 + 12 +1 subject to |11| + |221 + + 10 VI VI ALAL
(c) minimize xy + 2x122 + 2x3 + x3 + 3x1 – 4x2

Answer 1

To check if a problem is convex, examine the objective function and constraints. Write a CVX code that solves the problem. Obtain the optimal solution by running CVX with given values.

Step-by-step explanation:

(a) Check if problem is convex:

To check if a problem is convex, we need to examine its objective function and constraints. In this case, the objective function is linear (||Ax - b||) and the constraint (Ax) is also linear. Since the objective function and constraints are both linear, the problem is convex.

(b) CVX code:

To write a CVX code that solves the problem, you need to provide the complete code including the definition of the variables and the constraints. However, I can give you an example:

cvx_begin
variables x(2)
minimize(norm(A * x - b))
cvx_end

(c) Optimal solution:

To obtain the optimal solution by running CVX, you need to input the values of A and b into the code and run it. The output will give you the optimal solution for x.