I am currently following the course: EE364A - Convex Optimization I
I have a question about one of the exercises which I have been struggling to solve. It is an optimization problem and should be rather simple but it aint that simple for me.
The exercise is as follows:
4.1 Consider the optimization problem
\begin{align} \text{minimize} & \quad f_0(x_1,x_2) \\ \text{subject to} & \quad 2x_1 + x_2 >= 1 \\ & \quad x_1 + 3x_2 >= 1 \\ & \quad x_1 >= 0, x_2 >= 0 \end{align} Make a sketch of the feasible set. For each of the following objective functions, give the optimal set and the optimal value. \begin{align} \text{(a)} & \quad f_0(x_1,x_2) = x_1 + x_2 \\ \text{(b)} & \quad f_0(x_1,x_2) = -x_1 - x_2 \\ \text{(c)} & \quad f_0(x_1,x_2) = x_1 \\ \text{(d)} & \quad f_0(x_1,x_2) = max\{x_1,x_2\} \\ \text{(e)} & \quad f_0(x_1,x_2) = x_1^2 + 9x_2^2 \end{align} My sketch is just like in the solution so ill just take that.
(a) I found this to be x* = [2/5, 1/5] which is the point where the two lines crosses.
(b)-(e) I haven't really figured how to solve. Could you guys give me a hint on how to solve them. The solution gives me the result but I don't understand them.
Would I be able to illustrate this in MATLAB? Or how can I easily see the answers to them?