Geodesic
Quantitative Results on Algorithms for Zeros of Differences of Monotone Operators in Hilbert Space
Journal of convex analysis, Tome 30 (2023) no. 1, pp. 295-315
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We provide quantitative information in the form of a rate of metastability in the sense of T. Tao and (under a metric regularity assumption) a rate of convergence for an algorithm approximating zeros of differences of maximally monotone operators due to A. Moudafi by using techniques from "proof mining", a subdiscipline of mathematical logic. For the rate of convergence, we provide an abstract and general result on the construction of rates of convergence for quasi-Fejér monotone sequences with metric regularity assumptions, generalizing previous results for Fejér monotone sequences due to U. Kohlenbach, G. López-Acedo and A. Nicolae.
Classification : 47H05, 47J25, 03F10, 47H09
Mots-clés : Maximally monotone operators, Zeros of set-valued operators, DC programming, Fejér monotonicity, proof mining 
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     author = {N. Pischke},
     title = {Quantitative {Results} on {Algorithms} for {Zeros} of {Differences} of {Monotone} {Operators} in {Hilbert} {Space}},
     journal = {Journal of convex analysis},
     pages = {295--315},
     year = {2023},
     volume = {30},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a15/}
}
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N. Pischke. Quantitative Results on Algorithms for Zeros of Differences of Monotone Operators in Hilbert Space. Journal of convex analysis, Tome 30 (2023) no. 1, pp. 295-315. http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a15/