A Proximal Point Algorithm Revisited and Extended

Gheorghe Moroşanu () and Adrian Petruşel ()
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Gheorghe Moroşanu: Academy of Romanian Scientists
Adrian Petruşel: Academy of Romanian Scientists

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 3, No 13, 1120-1129

Abstract: Abstract This note is a reaction to the recent paper by Rouhani and Moradi (J Optim Theory Appl 172:222–235, 2017), where a proximal point algorithm proposed by Boikanyo and Moroşanu (Optim Lett 7:415–420, 2013) is discussed. Noticing the inappropriate formulation of that algorithm, we propose a more general algorithm for approximating zeros of a maximal monotone operator on a Hilbert space. Besides the main result on the strong convergence of the sequences generated by this new algorithm, we discuss some particular cases, including the approximation of minimizers of convex functionals and present two examples to illustrate the applicability of the algorithm. The note clarifies and extends both the papers quoted above.

Keywords: Maximal monotone operator; Proximal point algorithm; Strong convergence; Convex function; 47J25; 47H05; 90C25; 90C90 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01536-5

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