Binary optimal control by trust-region steepest descent

• 成果类型: Article
• 署名作者: Hahn, Mirko; Leyffer, Sven; Sager, Sebastian
• 署名单位: Otto von Guericke University; United States Department of Energy (DOE); Argonne National Laboratory
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-021-01733-z
• 发表日期: 2023
• 页码: 147-190
• 关键词: Optimization; TOPOLOGY; equation; shape; time

摘要

We present a trust-region steepest descent method for dynamic optimal control problems with binary-valued integrable control functions. Our method interprets the control function as an indicator function of a measurable set and makes set-valued adjustments derived from the sublevel sets of a topological gradient function. By combining this type of update with a trust-region framework, we are able to show by theoretical argument that our method achieves asymptotic stationarity despite possible discretization errors and truncation errors during step determination. To demonstrate the practical applicability of our method, we solve two optimal control problems constrained by ordinary and partial differential equations, respectively, and one topological optimization problem.