Linear Systems Associated with Numerical Methods for Constrained Optimization

Abstract

Linear systems associated with numerical methods for constrained optimization are discussed 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 constrained optimization can be expressed as similar systems of linear equations. All these linear systems can be viewed as some kinds of approximation to the linear system derived by the Lagrange-Newton method. Some properties of these linear systems are analyzed.