An LP-Newton method: nonsmooth equations, KKT systems, and nonisolated solutions

• 成果类型: Article
• 署名作者: Facchinei, Francisco; Fischer, Andreas; Herrich, Markus
• 署名单位: Sapienza University Rome; Technische Universitat Dresden
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0676-6
• 发表日期: 2014
• 页码: 1-36
• 关键词: nonlinear complementarity-problem; local convergence properties; nash equilibrium problems; generalized equations; trust-region; algorithm; identification; optimization; FRAMEWORK; sqp

摘要

We define a new Newton-type method for the solution of constrained systems of equations and analyze in detail its properties. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, the method converges locally quadratically to a solution of the system, thus filling an important gap in the existing theory. The new algorithm improves on known methods and, when particularized to KKT systems derived from optimality conditions for constrained optimization or variational inequalities, it has theoretical advantages even over methods specifically designed to solve such systems.