Solution: Constrained Optimization

Explanation

In the portfolio optimization problem,$x_1,x_2,x_3$ denote the fraction of each stock (STK1, STK2, STK3) in the portfolio. The goal is to maximize the diversity of the portfolio given by the EMP.

An EMP can be written as a standard minimization problem as follows:

where $A \in \R^{m \times d}$ is the constraint matrix with the $m$ constraints and $b \in \R^m$ is the constraint vector.

In the portfolio optimization problem $x = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \in \R^3$ ...