Using the result of Exercise 13, it is possible to avoid the discontinuity at d = 0 in the direction

Using the result of Exercise 13, it is
possible to avoid the discontinuity at d = 0 in the direction finding mapping
of the simple gradient projection method. At a given point let γ = −
min{0, λi}, with the minimum taken with respect to the indices i
corresponding the active inequalities. The direction to be taken at this point
is d = −Pg if |Pg| γ , or d, defined by dropping the inequality i
for which λi = −γ , if |Pg| γ . (In case of equality
either direction is selected.) Show that this direction finding map is closed
over a region where the set of active inequalities does not change.