A mesh-independence result for semismooth Newton methods

• 成果类型: Article; Proceedings Paper
• 署名作者: Hintermüller, M; Ulbrich, M
• 署名单位: University of Graz; Rice University; University of Hamburg
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-004-0540-9
• 发表日期: 2004
• 页码: 151-184
• 关键词: operator-equations; CONVERGENCE; approximation; PRINCIPLE

摘要

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.