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Volume 23, Issue 3
Preconditioned Spectral Projected Gradient Method on Convex Sets

Lenys Bello & Marcos Raydan

J. Comp. Math., 23 (2005), pp. 225-232.

Published online: 2005-06

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  • Abstract

The spectral gradient method has proved to be effective for solving large-scale unconstrained optimization problems. It has been recently extended and combined with the projected gradient method for solving optimization problems on convex sets. This combination includes the use of nonmonotone line search techniques to preserve the fast local convergence. In this work we further extend the spectral choice of steplength to accept preconditioned directions when a good preconditioner is available. We present an algorithm that combines the spectral projected gradient method with preconditioning strategies to increase the local speed of convergence while keeping the global properties. We discuss implementation details for solving large-scale problems.  

  • Keywords

Spectral gradient method, Projected gradient method, Preconditioning techniques, Nonmonotone line search.

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COPYRIGHT: © Global Science Press

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@Article{JCM-23-225, author = {Lenys Bello and Marcos Raydan}, title = {Preconditioned Spectral Projected Gradient Method on Convex Sets}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {3}, pages = {225--232}, abstract = {

The spectral gradient method has proved to be effective for solving large-scale unconstrained optimization problems. It has been recently extended and combined with the projected gradient method for solving optimization problems on convex sets. This combination includes the use of nonmonotone line search techniques to preserve the fast local convergence. In this work we further extend the spectral choice of steplength to accept preconditioned directions when a good preconditioner is available. We present an algorithm that combines the spectral projected gradient method with preconditioning strategies to increase the local speed of convergence while keeping the global properties. We discuss implementation details for solving large-scale problems.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8811.html} }
TY - JOUR T1 - Preconditioned Spectral Projected Gradient Method on Convex Sets AU - Lenys Bello & Marcos Raydan JO - Journal of Computational Mathematics VL - 3 SP - 225 EP - 232 PY - 2005 DA - 2005/06 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8811.html KW - Spectral gradient method, Projected gradient method, Preconditioning techniques, Nonmonotone line search. AB -

The spectral gradient method has proved to be effective for solving large-scale unconstrained optimization problems. It has been recently extended and combined with the projected gradient method for solving optimization problems on convex sets. This combination includes the use of nonmonotone line search techniques to preserve the fast local convergence. In this work we further extend the spectral choice of steplength to accept preconditioned directions when a good preconditioner is available. We present an algorithm that combines the spectral projected gradient method with preconditioning strategies to increase the local speed of convergence while keeping the global properties. We discuss implementation details for solving large-scale problems.  

Lenys Bello and Marcos Raydan. (2005). Preconditioned Spectral Projected Gradient Method on Convex Sets. Journal of Computational Mathematics. 23 (3). 225-232. doi:
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