Portfolio Optimization

170 Determination of the Entire Efficient Frontier Chap. 8

If t

j+1

=

˜

t

j+1

, and

˜

t

j+1

< ∞ let k

l

1

be defined by (8.10). Then the

multiplier for constraint k

l

1

is reduced to zero at t = t

j+1

and would

become strictly negative if t were allowed to increase beyond t

j+1

. In

this case we delete k

l

1

from the active set K

j

to obtain the new active

set K

j+1

. That is, we set K

j+1

= K

j

− {k

l

1

}.

If t

j+1

=

ˆ

t

j+1

and

ˆ

t

j+1

< ∞, let l

2

be defined by (8.15) . Then

inequality constraint l

2

, which was inactive at t

j

, becomes active when

t = t

j+1

. If t were allowed to increase beyond

ˆ

t

j+1

, t hen inequality

constraint i

2

would become violated. In this case, we add l

2

to K

j

to

form the new activ ...