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Linear systems associated with numerical methods for constrained optimization arediscussed in this paper. It is shown that the corresponding subproblems arise in most well-known methods, no matter line search methods or trust region methods for constrainedoptimization can be expressed as similar systems of linear equations. All these linearsystems can be viewed as some kinds of approximation to the linear system derived by theLagrange-Newton method. Some properties of these linear systems are analyzed.