Parabolic optimal control problems with combinatorial switching constraints, part III: branch-and-bound algorithm

被引：0

作者：

Buchheim, Christoph ^{[1
]}

Gruetering, Alexandra ^{[1
]}

Meyer, Christian ^{[1
]}

机构：

[1] TU Dortmund Univ, Dept Math, Dortmund, Germany

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2025年 / 90卷 / 03期

关键词：

PDE-constrained optimization; Switching time optimization; Global optimization; Branch-and-bound; TIME OPTIMIZATION;

D O I：

10.1007/s10589-025-00654-3

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given tolerance epsilon > 0, we show how to compute in finite time an epsilon-optimal solution in function space, independently of any prior discretization. The main ingredients in our approach are an appropriate branching strategy in infinite dimension, an a posteriori error estimation in order to obtain safe dual bounds, and an adaptive refinement strategy in order to allow arbitrary switching points in the limit. The performance of our approach is demonstrated by extensive experimental results.

引用

页码：649 / 689

页数：41