2025/01/03 by Pham Duy Khanh, Khanh, Pham Duy, Boris S. Mordukhovich +5
Engineering · Mathematics · #49J52 #49J53 #90C31 #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods for differential equations #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2501.02067
openalex publication_date 2025/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the concepts of generalized twice differentiability and quadratic bundles of nonsmooth functions that have been very recently proposed by Rockafellar in the framework of second-order variational analysis. These constructions, in contrast to second-order subdifferentials, are defined in primal spaces. We develop new techniques to study generalized twice differentiability for a broad class of prox-regular functions, establish their novel characterizations. Subsequently, quadratic bundles of prox-regular functions are shown to be nonempty, which provides the ground of potential applications in variational analysis and optimization.