On the Proximal Point Algorithm

B. Djafari Rouhani () and H. Khatibzadeh
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B. Djafari Rouhani: University of Texas at El Paso
H. Khatibzadeh: Tarbiat Modarres University

Journal of Optimization Theory and Applications, 2008, vol. 137, issue 2, No 10, 417 pages

Abstract: Abstract Let A be a maximal monotone operator in a real Hilbert space H and let {u n } be the sequence in H given by the proximal point algorithm, defined by u n =(I+c n A)−1(u n−1−f n ), ∀ n≥1, with u 0=z, where c n >0 and f n ∈H. We show, among other things, that under suitable conditions, u n converges weakly or strongly to a zero of A if and only if lim inf n→+∞|w n |

Keywords: Proximal-point algorithms; Variational inequalities; Ergodic theorems; Maximal monotone operators; Asymptotic centers (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-007-9329-3

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