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Volume 25, Issue 2
A Note on the Gradient Projection Method with Exact Stepsize Rule

Naihua Xiu, Changyu Wang & Lingchen Kong

J. Comp. Math., 25 (2007), pp. 221-230.

Published online: 2007-04

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  • Abstract

In this paper, we give some convergence results on the gradient projection method with exact stepsize rule for solving the minimization problem with convex constraints. Especially, we show that if the objective function is convex and its gradient is Lipschitz continuous, then the whole sequence of iterations produced by this method with bounded exact stepsizes converges to a solution of the concerned problem.

  • Keywords

Gradient projection method, Exact stepsize rule, Full convergence.

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COPYRIGHT: © Global Science Press

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@Article{JCM-25-221, author = {Naihua Xiu, Changyu Wang and Lingchen Kong}, title = {A Note on the Gradient Projection Method with Exact Stepsize Rule}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {2}, pages = {221--230}, abstract = {

In this paper, we give some convergence results on the gradient projection method with exact stepsize rule for solving the minimization problem with convex constraints. Especially, we show that if the objective function is convex and its gradient is Lipschitz continuous, then the whole sequence of iterations produced by this method with bounded exact stepsizes converges to a solution of the concerned problem.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8687.html} }
TY - JOUR T1 - A Note on the Gradient Projection Method with Exact Stepsize Rule AU - Naihua Xiu, Changyu Wang & Lingchen Kong JO - Journal of Computational Mathematics VL - 2 SP - 221 EP - 230 PY - 2007 DA - 2007/04 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8687.html KW - Gradient projection method, Exact stepsize rule, Full convergence. AB -

In this paper, we give some convergence results on the gradient projection method with exact stepsize rule for solving the minimization problem with convex constraints. Especially, we show that if the objective function is convex and its gradient is Lipschitz continuous, then the whole sequence of iterations produced by this method with bounded exact stepsizes converges to a solution of the concerned problem.

Naihua Xiu, Changyu Wang and Lingchen Kong. (2007). A Note on the Gradient Projection Method with Exact Stepsize Rule. Journal of Computational Mathematics. 25 (2). 221-230. doi:
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