This thesis mainly studies formulae of ABS updating matrices when parameter matrices are perturbed. The main results obtained in the thesis may be summarized as follows:1. New ABS updating formulae are derived and properties of ABS algorithm are discussed, especially when parameter matrices are perturbed.2. Right and left inverse matrices of parameter matrices are proposed and their updating formulae are also derived. Furthermore, applications of these formulae to constructing feasible directions and estimating multipliers are discussed. |