Averaged Mappings and the Gradient-Projection Algorithm

Hong-Kun Xu ()
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Hong-Kun Xu: National Sun Yat-sen University

Journal of Optimization Theory and Applications, 2011, vol. 150, issue 2, No 10, 360-378

Abstract: 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.

Keywords: Averaged mapping; Gradient-projection algorithm; Constrained convex minimization; Maximal monotone operator; Relaxed gradient-projection algorithm; Regularization; Minimum-norm (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (20)

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DOI: 10.1007/s10957-011-9837-z

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