Geodesic
A Hybrid Semismooth Quasi-Newton Method for Structured Nonsmooth Operator Equations in Banach Spaces
Journal of convex analysis, Tome 29 (2022) no. 1, pp. 183-204
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We present an algorithm for the solution of structured nonsmooth operator equations in Banach spaces. Specifically, we seek roots of mappings that involve the composition of a smooth outer and a semismooth inner map. To exploit this structure we propose a hybrid approach in which the semismooth part is linearized in the same way as in semismooth Newton methods while the smooth part is handled by a Broyden-like method. The resulting algorithm is a semismooth Newton-type method that does not require the evaluation of the derivative of the smooth part.
Classification : 47J25, 47N10, 49J27, 49J52, 49M15, 49M27, 65J15, 90C30, 90C48, 90C53, 90C56
Mots-clés : Semismooth Newton-type methods, Broyden-like method, quasi-Newton methods, superlinear convergence, nonsmooth operator equations 
@article{JCA_2022_29_1_JCA_2022_29_1_a10,
     author = {F. Mannel and A. Rund},
     title = {A {Hybrid} {Semismooth} {Quasi-Newton} {Method} for {Structured} {Nonsmooth} {Operator} {Equations} in {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {183--204},
     year = {2022},
     volume = {29},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a10/}
}
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%D 2022
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F. Mannel; A. Rund. A Hybrid Semismooth Quasi-Newton Method for Structured Nonsmooth Operator Equations in Banach Spaces. Journal of convex analysis, Tome 29 (2022) no. 1, pp. 183-204. http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a10/