Simple examples for the failure of Newton's method with line search for strictly convex minimization

• 成果类型: Article
• 署名作者: Jarre, Florian; Toint, Philippe L.
• 署名单位: Heinrich Heine University Dusseldorf; University of Namur
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0913-2
• 发表日期: 2016
• 页码: 23-34
• 关键词: nonstationary points; CONVERGENCE

摘要

In this paper two simple examples of a twice continuously differentiable strictly convex function are presented for which Newton's method with line search converges to a point where the gradient of is not zero. The first example uses a line search based on the Wolfe conditions. For the second example, some strictly convex function is defined as well as a sequence of descent directions for which exact line searches do not converge to the minimizer of . Then is perturbed such that these search directions coincide with the Newton directions for the perturbed function while leaving the exact line search invariant.