The numerical solution of Newton's problem of least resistance

• 成果类型: Article
• 署名作者: Wachsmuth, Gerd
• 署名单位: Technische Universitat Chemnitz
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0756-2
• 发表日期: 2014
• 页码: 331-350
• 关键词: variational-problems; minimal resistance; convex-functions

摘要

In this paper we consider Newton's problem of finding a convex body of least resistance. This problem could equivalently be written as a variational problem over concave functions in . We propose two different methods for solving it numerically. First, we discretize this problem by writing the concave solution function as a infimum over a finite number of affine functions. The discretized problem could be solved by standard optimization software efficiently. Second, we conjecture that the optimal body has a certain structure. We exploit this structure and obtain a variational problem in . Deriving its Euler-Lagrange equation yields a program with two unknowns, which can be solved quickly.