GLOBAL CONVERGENCE OF DAMPED NEWTON METHOD FOR NONSMOOTH EQUATIONS VIA THE PATH SEARCH

• 成果类型: Article
• 署名作者: RALPH, D
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.19.2.352
• 发表日期: 1994
• 页码: 352-389
• 关键词: monotone variational-inequalities; nonlinear complementarity-problem; generalized equations; normal maps; sensitivity; algorithms; PROGRAMS

摘要

A natural damping of Newton's method for nonsmooth equations is presented. This damping, via the path search instead of the traditional line search, enlarges the domain of convergence of Newton's method and therefore is said to be globally convergent. Convergence behavior is like that of line search damped Newton's method for smooth equations, including Q-quadratic convergence rates under appropriate conditions. Applications of the path search include damping Robinson-Newton's method for nonsmooth normal equations corresponding to nonlinear complementarity problems and variational inequalities, hence damping both Wilson's method (sequential quadratic programming) for nonlinear programming and Josephy-Newton's method for generalized equations. Computational examples from nonlinear programming