A mesh-independence result for semismooth Newton methods
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- Hintermüller, M. & Ulbrich, M. Math. Program., Ser. A (2004) 101: 151. doi:10.1007/s10107-004-0540-9
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For a class of semismooth operator equations a mesh independence result for generalized Newton methods is established. The main result states that the continuous and the discrete Newton process, when initialized properly, converge q-linearly with the same rate. The problem class considered in the paper includes MCP-function based reformulations of first order conditions of a class of control constrained optimal control problems for partial differential equations for which a numerical validation of the theoretical results is given.