Abstract
It is well known that the gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. In this article, we first provide an alternative averaged mapping approach to the GPA. This approach is operator-oriented in nature. Since, in general, in infinite-dimensional Hilbert spaces, GPA has only weak convergence, we provide two modifications of GPA so that strong convergence is guaranteed. Regularization is also applied to find the minimum-norm solution of the minimization problem under investigation.
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Communicated by J.-C. Yao.
The author would like to thank the referees for their helpful comments on this manuscript. He was supported in part by NSC 97-2628-M-110-003-MY3.
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Xu, HK. Averaged Mappings and the Gradient-Projection Algorithm. J Optim Theory Appl 150, 360–378 (2011). https://doi.org/10.1007/s10957-011-9837-z
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DOI: https://doi.org/10.1007/s10957-011-9837-z