Portfolio Optimization

Sec. 6.2 Computer Programs 127

appropriate version of the Sherman and Morrison [23] and Woodbury

[25] update formula, H

j+1

can be determined from H

j

in approximately

p

2

operations, a considerable saving. Similar savings can be obtained

using matrix factorizations.

Continuing the analysis with H

j

being (p, p), solving the linear equa-

tions takes about p

2

computations. Computation o f the maximum feasi-

ble step size takes about 2mn operations, although this could be smaller

if some of the constraints were simple lower and upper bounds. All other

computations require order n or m calculations. Consequently, solving

linear equations with coefficient matrix H