The Quadratic Programming Algorithm GRQP

Subroutine GRQP minimizes the quadratic function S 6) of Eq. (6.3-7) over the feasible region 

The basis set 6 of estimated parameters, obtained by solving the corresponding rows of Eq. (6.3-10). Nonzero entries i in the vector LBAS identify these parameters, whose current values are stored in the vector PAR at the end of each transformation. 

A set 6c of actively constrained parameters, which currently lie at a limit of Eq. (6.4-2). Nonzero entries i or —i in the vector LBOX identify any such parameters and the active limit (upper or lower) for each. 

The set Of of free parameters (all others). These parameters are candidates for transfer into Og or 6c in the next transformation. 

Each step in the minimization begins with a search for a descent variable 6i among the candidate set composed of 6f plus any members of 6c that lie at an uphill limit. The candidate 6i with the largest test divisor Di = Aii /Aureal is chosen, provided that Dj exceeds the threshold tolerance ADTOL and that the test values Dj = / ADAjj,cci) for the resulting inverse matrix all exceed ADTOL. When such a candidate is found, one of the following moves is made  

---