Abstract
To guarantee global convergence of the standard (unmodified) PRP nonlinear conjugate gradient method for unconstrained optimization, the exact line search or some Armijo type line searches which force the PRP method to generate descent directions have been adopted. In this short note, we propose a non-descent PRP method in another way. We prove that the unmodified PRP method converges globally even for nonconvex minimization by the use of an approximate descent inexact line search.
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This work was supported by the NSF foundation (10901026) of China, The Open Fund Project of Key Research Institute of Philosophies and Social Sciences in Hunan Universities and the Key Project of the Scientific Research Fund of the Hunan Provincial Education Department.
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Zhou, W. A short note on the global convergence of the unmodified PRP method. Optim Lett 7, 1367–1372 (2013). https://doi.org/10.1007/s11590-012-0511-7
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DOI: https://doi.org/10.1007/s11590-012-0511-7