Linear Systems Associated with Numerical Methods for Constrained Opitmization
Y. Yuan 11 State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, P. O. Box 2719, Beijing 100080, China
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 van be expressed as similar systems of linear epuations. 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.
Key words: Constrained optimization; Linear equations; Lagrange-Newton method; Trust region; Line search.