2020/06/22 by Amos Uderzo, Uderzo, Amos
Computer Science · Decision Sciences · Engineering · Mathematics · #49J53 #Advanced Optimization Algorithms Research #Constraint Satisfaction and Optimization #FOS: Mathematics #Functional Analysis (math.FA) #Multi-Criteria Decision Making #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2006.12142
openalex publication_date 2020/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper, several properties concerning generalized derivatives\nof multifunctions implicitly defined by set-valued inclusions are studied by\ntechniques of variational analysis. Set-valued inclusions are problems\nformalizing the robust fulfilment of cone constraint systems, whose data are\naffected by a "crude knowledge" of uncertain elements, so they can not be\ncasted in traditional generalized equations.\n The focus of this study in on the first-order behaviour of the solution\nmapping associated with a parameterized set-valued inclusion, starting with\nLipschitzian properties and then considering its graphical derivative. In\nparticular, a condition for the Aubin continuity of the solution mapping is\nestablished in terms of outer prederivative of the set-valued mapping defining\nthe inclusion. A large class of parameterized set-valued inculsions is singled\nout, whose solution mapping turns out to be convex. Some relevant consequences\non the graphical derivative are explored. In the absence of that, formulae for\nthe inner and outer approximation of the graphical derivative are provided by\nmeans of prederivatives of the problem data. A representation useful to\ncalculate the coderivative of the solution mapping is also obtained via the\nsubdifferential of a merit function.\n