Portfolio Optimization

Sec. 6.3 Exercises 13 7

(b) Now assume that x

1

is a quasi-stationary point for (6.1)

and that A

1

is obtained fro m A

0

by deleting row k where

(v

0

)

k

> 0. Show g

′

1

s

1

> 0 where s

1

is obtained from the

solution of



C A

′

1

A

1

0



s

1

v

1



=



g

1

0



.

6.2 Let x

0

, s

0

and f(x) be as in the discussion leading to (6.9). Show

that f(x

0

− σs

0

) is a decreasing function of σ for σ ∈ [0, 1] and

attains its minimum at σ = 1. (Hint: Use Lemma 6.1.)

6.3 (a) Apply QPSolver (by hand) to Example 5.2 using x

0

= (1, 1)

′

.

(b) Verify your results for part ( a) by using the QPSolver pro-

gram as in Example 6.3 (Figure 6.3).

6.4 (a) Apply QPSolver (by hand) to Example 5.2 using x

0

= (1, 0)

′

.

(b) Verify ...