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Volume 19, Issue 3
A Robust Trust Region Algorithm for Solving General Nonlinear Programming

Xin-Wei Liu & Ya-Xiang Yuan

J. Comp. Math., 19 (2001), pp. 309-322.

Published online: 2001-06

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  • Abstract

The trust region approach has been extended to solving nonlinear constrained optimization. Most of these extensions consider only equality constraints and require strong global regularity assumptions. In this paper, a trust region algorithm for solving general nonlinear programming is presented, which solves an unconstrained piecewise quadratic trust region subproblem and a quadratic programming trust region subproblem at each iteration. A new technique for updating the penalty parameter is introduced. Under very mild conditions, the global convergence results are proved. Some local convergence results are also proved. Preliminary numerical results are also reported.  

  • Keywords

Trust region algorithm, Nonlinear programming.

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-309, author = {Liu , Xin-Wei and Yuan , Ya-Xiang}, title = {A Robust Trust Region Algorithm for Solving General Nonlinear Programming}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {3}, pages = {309--322}, abstract = {

The trust region approach has been extended to solving nonlinear constrained optimization. Most of these extensions consider only equality constraints and require strong global regularity assumptions. In this paper, a trust region algorithm for solving general nonlinear programming is presented, which solves an unconstrained piecewise quadratic trust region subproblem and a quadratic programming trust region subproblem at each iteration. A new technique for updating the penalty parameter is introduced. Under very mild conditions, the global convergence results are proved. Some local convergence results are also proved. Preliminary numerical results are also reported.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8983.html} }
TY - JOUR T1 - A Robust Trust Region Algorithm for Solving General Nonlinear Programming AU - Liu , Xin-Wei AU - Yuan , Ya-Xiang JO - Journal of Computational Mathematics VL - 3 SP - 309 EP - 322 PY - 2001 DA - 2001/06 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8983.html KW - Trust region algorithm, Nonlinear programming. AB -

The trust region approach has been extended to solving nonlinear constrained optimization. Most of these extensions consider only equality constraints and require strong global regularity assumptions. In this paper, a trust region algorithm for solving general nonlinear programming is presented, which solves an unconstrained piecewise quadratic trust region subproblem and a quadratic programming trust region subproblem at each iteration. A new technique for updating the penalty parameter is introduced. Under very mild conditions, the global convergence results are proved. Some local convergence results are also proved. Preliminary numerical results are also reported.  

Liu , Xin-Wei and Yuan , Ya-Xiang. (2001). A Robust Trust Region Algorithm for Solving General Nonlinear Programming. Journal of Computational Mathematics. 19 (3). 309-322. doi:
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