A new inertial-type hybrid projection-proximal algorithm for monotone inclusions |
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Authors: | Paul-Emile Maingé Nora Merabet |
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Institution: | a Laboratoire CEREGMIA, Université des Antilles et de la Guyane, D.S.I., Campus de Schoelcher, 97233 Cedex, Martinique (F.W.I.), France b United Arab Emirates University, College of Science, Department of Mathematical Sciences, P.O. Box 17551, Al-Ain, United Arab Emirates |
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Abstract: | This paper investigates an enhanced proximal algorithm with interesting practical features and convergence properties for solving non-smooth convex minimization problems, or approximating zeroes of maximal monotone operators, in Hilbert spaces. The considered algorithm involves a recent inertial-type extrapolation technique, the use of enlargement of operators and also a recently proposed hybrid strategy, which combines inexact computation of the proximal iteration with a projection. Compared to other existing related methods, the resulting algorithm inherits the good convergence properties of the inertial-type extrapolation and the relaxed projection strategy. It also inherits the relative error tolerance of the hybrid proximal-projection method. As a special result, an update of inexact Newton-proximal method is derived and global convergence results are established. |
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Keywords: | Convex minimization Maximal monotone operator Proximal point algorithm Inexact computations Inertial extrapolation Inexact Newton method |
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