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dc.contributor.authorUlbrich, Michael
dc.date.accessioned 2018-06-18T17:48:13Z
dc.date.available 2018-06-18T17:48:13Z
dc.date.issued 2000-04
dc.identifier.citation Ulbrich, Michael. "Semismooth Newton Methods for Operator Equations in Function Spaces." (2000) https://hdl.handle.net/1911/101940.
dc.identifier.urihttps://hdl.handle.net/1911/101940
dc.description.abstract We develop a semismoothness concept for nonsmooth superposition operators in function spaces. The considered class of operators includes NCP-function-based reformulations of infinite-dimensional nonlinear complementarity problems, and thus covers a very comprehensive class of applications. Our results generalize semismoothness and alpha-order semismoothness from finite-dimensional spaces to a Banach space setting. Hereby, a new generalized differential is used that can be seen as an extension of Qi's finite-dimensional C-subdifferential to our infinite-dimensional framework. We apply these semismoothness results to develop a Newton-like method for nonsmooth operator equations and prove its local q-superlinear convergence to regular solutions. If the underlying operator is alpha-order semismoothness, convergence of q-order 1+alpha is proved. We also establish the semismoothness of composite operators and develop corresponding chain rules. The developed theory is accompanied by illustrating examples and by applications to nonlinear complementarity problems.
dc.format.extent 31 pp
dc.title Semismooth Newton Methods for Operator Equations in Function Spaces
dc.type Technical report
dc.date.note April 2000
dc.identifier.digital TR00-11
dc.type.dcmi Text


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