1 dT1 Ab2 is the result of replacing the (invisible) identity matrix in dT1 Ib2 by A. The terms A-orthogonal and A-conjugate vectors are also used in literature.
2 with positive definite Hessian, as usual
3 It is possible to associate certain distance functions or metrics with the search directions different optimization methods pick up. For quasi-Newton methods, the underlying positive definite weight matrix and hence the corresponding metric definition change from iteration to iteration. Therefore, they are also called variable metric methods.