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Volume 9, Issue 4
A Dual Algorithm for Minimizing a Quadratic Function with Two Quadratic Constraints

Ya-Xiang Yuan

J. Comp. Math., 9 (1991), pp. 348-359.

Published online: 1991-09

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  • Abstract

In this paper, we present a dual algorithm for minimizing a convex quadratic function with two quadratic constraints. Such a minimization problem is a subproblem that appears in some trust region algorithms for general nonlinear programming. Some theoretical properties of the dual problem are given. Global convergence of the algorithm is proved and a local superlinear convergence result is presented. Numerical examples are also provided.

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@Article{JCM-9-348, author = {Yuan , Ya-Xiang}, title = {A Dual Algorithm for Minimizing a Quadratic Function with Two Quadratic Constraints}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {4}, pages = {348--359}, abstract = {

In this paper, we present a dual algorithm for minimizing a convex quadratic function with two quadratic constraints. Such a minimization problem is a subproblem that appears in some trust region algorithms for general nonlinear programming. Some theoretical properties of the dual problem are given. Global convergence of the algorithm is proved and a local superlinear convergence result is presented. Numerical examples are also provided.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9410.html} }
TY - JOUR T1 - A Dual Algorithm for Minimizing a Quadratic Function with Two Quadratic Constraints AU - Yuan , Ya-Xiang JO - Journal of Computational Mathematics VL - 4 SP - 348 EP - 359 PY - 1991 DA - 1991/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9410.html KW - AB -

In this paper, we present a dual algorithm for minimizing a convex quadratic function with two quadratic constraints. Such a minimization problem is a subproblem that appears in some trust region algorithms for general nonlinear programming. Some theoretical properties of the dual problem are given. Global convergence of the algorithm is proved and a local superlinear convergence result is presented. Numerical examples are also provided.

Yuan , Ya-Xiang. (1991). A Dual Algorithm for Minimizing a Quadratic Function with Two Quadratic Constraints. Journal of Computational Mathematics. 9 (4). 348-359. doi:
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