Global optimization in Hilbert space

• 成果类型: Article
• 署名作者: Houska, Boris; Chachuat, Benoit
• 署名单位: ShanghaiTech University; Imperial College London
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1215-7
• 发表日期: 2019
• 页码: 221-249
• 关键词: convex computation; approximations; intersection; integration; Ellipsoids; algorithm; cut; set

摘要

We propose a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. Because these run-time bounds are independent of the number of optimization variables and, in particular, are valid for optimization problems with infinitely many optimization variables, we prove that the algorithm converges to an epsilon-suboptimal global solution within finite run-time for any given termination tolerance epsilon>0. Finally, we illustrate these results for a problem of calculus of variations.