2022/12/23 by Paul Manns, Manns, Paul, Schiemann, Annika · 1 citation
Computer Science · Medicine · #49K30 #49M05 #49M37 #49Q15 #Aortic aneurysm repair treatments #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2212.12226
openalex publication_date 2022/12/23 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28
We consider optimal control problems with integer-valued controls and a total variation regularization penalty in the objective on domains of dimension two or higher. The penalty yields that the feasible set is sequentially closed in the weak-^* and closed in the strict topology in the space of functions of bounded variation. In turn, we derive first-order optimality conditions of the optimal control problem as well as trust-region subproblems with partially linearized model functions using local variations of the level sets of the feasible control functions. We also prove that a recently proposed function space trust-region algorithm -- sequential linear integer programming -- produces sequences of iterates whose limits are first-order optimal points.