2016/10/24 by Davide Barilari, Barilari, Davide, Francesco Boarotto +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.DG #math.OC
paper · pdf · doi:10.48550/arxiv.1610.07556
20 pages, 2 figures
openalex publication_date 2016/10/24 · arxiv created 2017/07/01 · arxiv updated 2017/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the regularity properties of the value function associated with an affine optimal control problem with quadratic cost plus a potential, for a fixed final time and initial point. Without assuming any condition on singular minimizers, we prove that the value function is continuous on an open and dense subset of the interior of the attainable set. As a byproduct we obtain that it is actually smooth on a possibly smaller set, still open and dense.