
254 Introduction to Linear Optimization and Extensions with MATLAB
R
for the investor. To this end, the investor specifies a constraint that forces her
portfolio selection to achieve at least a certain amount of expected return R.
That is, the investor enforces the constraint
E(r
p
) =
n
P
i=1
µ
i
x
i
≥ R.
Markowitz Portfolio Selection Model
Now all of the components are in place for specification of the Markowitz
portfolio model, also known as mean-variance optimization (MVO). The most
well-known version of the MVO model has the objective of minimizing the
variance of the portfolio and is given as follows
minimize
n
P
i=1
n
P
j=1
σ
ij
x
i
x
j
subject to
n
P
i=1
µ
i
x
i
≥ R
n
P
i=1
x
i
= 1 ...