Portfolio Optimization

132 A QP Solution Algorithm Chap. 6

41 while flag == 0

42 QPStep1

43 QPStep2

44 QPStep3

45 end

46

47 minvalue = fxj;

48 minimizer = xj;

49 IndexSet = Kj;

50 multipliers = uj;

Figure 6.5 QPSolver.m.

QPStep1.m (Figure 6.6 ) implements Step 1 of QPSolver. Line 3

constructs

Hj =



BigC Aj

′

Aj 0



,

and line 4 constructs

rhs =



gxj

0



.

Line 5 solves the linear equations Hj y = rhs. Line 6 extracts the first n

components into sj and line 7 extracts the last active components into

vj.

1 %Q PStep1.m

2 %S tep 1: Computation of Search Direction sj.

3 Hj = ve rtcat([BigC Aj'],[Aj ze ros(active,active)]);

4 rh s = vertcat(gxj, zeros(active,1));

5 y = Hjˆ−1

*

rhs;

6 sj = y(1:n);

7 vj = y(n+1:n+active); ...