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 - <p style="text-align: justify;">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. &nbsp;</p>