2023/10/15 by Monica Motta, Motta, Monica, Franco Rampazzo +1
Computer Science · Mathematics · #49-02 #49K15 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2310.09845
openalex publication_date 2023/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article makes no claim to originality, other than, perhaps, the simple statement here called the \it Abstract Maximum Principle. Actually, the whole contents are strongly based on some H. Sussmann's and coauthors' papers, in which, in a much more general context, the set-separation approach is regarded as foundational for necessary conditions for minima. So, rather than being the exposition of original material, this paper has mainly a pedagogical purpose. From the Abstract Maximum Principle it is possible to deduce several necessary conditions for both finite dimensional minimum problems and for optimal control problems. More in general, this Principle seems apt to capture some consequences of the geometric and topological idea of (possibly vector-valued) minimization in a parametrized problem.