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Volume 21, Issue 1
Linear Systems Associated with Numerical Methods for Constrained Optimization

Y. Yuan

J. Comp. Math., 21 (2003), pp. 71-84.

Published online: 2003-02

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  • 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.  

  • Keywords

Constrained optimization, Linear equations, Lagrange-Newton method, Trust region, Line search.

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COPYRIGHT: © Global Science Press

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@Article{JCM-21-71, author = {Y. Yuan}, title = {Linear Systems Associated with Numerical Methods for Constrained Optimization}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {1}, pages = {71--84}, 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.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10284.html} }
TY - JOUR T1 - Linear Systems Associated with Numerical Methods for Constrained Optimization AU - Y. Yuan JO - Journal of Computational Mathematics VL - 1 SP - 71 EP - 84 PY - 2003 DA - 2003/02 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10284.html KW - Constrained optimization, Linear equations, Lagrange-Newton method, Trust region, Line search. AB -

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.  

Y. Yuan. (2003). Linear Systems Associated with Numerical Methods for Constrained Optimization. Journal of Computational Mathematics. 21 (1). 71-84. doi:
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