Most of NLP linearisation algorithms from ASAI are based on QP, not LP subproblems. I have tried some lp-based and I'm not fond of results - convergence isn't good enough.
So I have started to implement QP class (some code already have been added to svn; first of all I intend to connect cvxopt default qp solver). I had spent much time thinking what is the best letter for the QP matrix: MATLAB uses H, cvxopt - P, TOMLAB uses F, etc, etc.
I desided to chose H, because it seems the most pretty to me, however, the drawback of the latter - some people can associate the one with Hesse matrix (for example, TOMLAB uses the notation). In OO Hesse matrix will be passed as d2f (also I intend to implement d2c, d2h, d2L), for example:
p = NLP(..., c=myIneqConstr, dc=myDIneqConstr, d2c=myD2IneqConstr)
p.h = myEqConstr
p.dh = myDEqConstr
p.d2h = myD2EqConstr
(myIneqConstr etc are names of corresponding functions).