Portfolio Optimization

180 Determination of the Entire Efficient Frontier Chap. 8

for all t ≥ 0, where A

j

and b

j

correspo nd to the active constraints for

the interval [t

j

, t

j+1

] determined by PQPSolver. Similarly, x

j+1

(t) is

optimal for

min{ − tµ

′

x +

1

2

x

′

Σx | A

j+1

x = b

j+1

} (8.26)

for all t ≥ 0, where A

j+1

and b

j+1

correspo nd to the active constraints

for the interval [t

j+1

, t

j+2

] determined by PQPSolver.

The analysis now continues according to how the end of the interval

[t

j

, t

j+1

] is determined in Step 3 of PQPSolver. If t

j+1

=

˜

t

j+1

, then

constraint k

l

1

is deleted from the active set for the next interval. If

t

j+1

=

ˆ

t

j+1

, then constraint l

2

is added to the active set for the next