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Zbl 1233.90280
Xu, Hong-Kun
Averaged mappings and the gradient-projection algorithm. (English)
[J] J. Optim. Theory Appl. 150, No. 2, 360-378 (2011). ISSN 0022-3239; ISSN 1573-2878/e

Author's 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.''
[Constantin Zălinescu (Iaşi)]

MSC 2000:: *90C48 Programming in abstract spaces

Keywords: averaged mapping; gradient-projection algorithm; constrained convex minimization; maximal monotone operator; relaxed gradient-projection algorithm; regularization; minimum-norm

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