Volume 20, Issue 3
An Interior Trust Region Algorithm for Nonlinear Minimization with Linear Constraints

Jian Guo Liu

DOI:

J. Comp. Math., 20 (2002), pp. 225-244

Published online: 2002-06

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  • Abstract

An interior trust-region-based algorithm for linearly constained minimization problems is proposed and analyzed. This algorithm is similar to trust region algorithms for unconstrained minimization: a trust region subproblem on a subspace is solved in each iteration.We establish that the proposed algorithm has convergence properties analogous point of the generated sequence satisfies the Krush-Kuhn-Tucker (KKT)conditions and at least one limit point satisfies second order necessary optimatity conditions. In addition, if one limit point is a strong local minimizer and the Hessian is Lipschitz continuous in a neighborbood of that point, then the generated sequence converges globally to that point in the rate of at least 2-step quadratic. We are mainly concerned with the theoretical properties of the algorithm in this paper. Implementation issues and adaptation to large-scale problems will be addressed in a future report.

  • Keywords

Nonlinear programming Linear constraints Trust region algorithms Newton methods

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@Article{JCM-20-225, author = {}, title = {An Interior Trust Region Algorithm for Nonlinear Minimization with Linear Constraints}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {3}, pages = {225--244}, abstract = { An interior trust-region-based algorithm for linearly constained minimization problems is proposed and analyzed. This algorithm is similar to trust region algorithms for unconstrained minimization: a trust region subproblem on a subspace is solved in each iteration.We establish that the proposed algorithm has convergence properties analogous point of the generated sequence satisfies the Krush-Kuhn-Tucker (KKT)conditions and at least one limit point satisfies second order necessary optimatity conditions. In addition, if one limit point is a strong local minimizer and the Hessian is Lipschitz continuous in a neighborbood of that point, then the generated sequence converges globally to that point in the rate of at least 2-step quadratic. We are mainly concerned with the theoretical properties of the algorithm in this paper. Implementation issues and adaptation to large-scale problems will be addressed in a future report. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8913.html} }
TY - JOUR T1 - An Interior Trust Region Algorithm for Nonlinear Minimization with Linear Constraints JO - Journal of Computational Mathematics VL - 3 SP - 225 EP - 244 PY - 2002 DA - 2002/06 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8913.html KW - Nonlinear programming KW - Linear constraints KW - Trust region algorithms KW - Newton methods AB - An interior trust-region-based algorithm for linearly constained minimization problems is proposed and analyzed. This algorithm is similar to trust region algorithms for unconstrained minimization: a trust region subproblem on a subspace is solved in each iteration.We establish that the proposed algorithm has convergence properties analogous point of the generated sequence satisfies the Krush-Kuhn-Tucker (KKT)conditions and at least one limit point satisfies second order necessary optimatity conditions. In addition, if one limit point is a strong local minimizer and the Hessian is Lipschitz continuous in a neighborbood of that point, then the generated sequence converges globally to that point in the rate of at least 2-step quadratic. We are mainly concerned with the theoretical properties of the algorithm in this paper. Implementation issues and adaptation to large-scale problems will be addressed in a future report.
Jian Guo Liu. (1970). An Interior Trust Region Algorithm for Nonlinear Minimization with Linear Constraints. Journal of Computational Mathematics. 20 (3). 225-244. doi:
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