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      Regular Subgradients of Marginal Functions with Applications to Calculus and Bilevel Programming

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          Abstract

          The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety of applications. Functions of this type are intrinsically nonsmooth and require the usage of tools of generalized differentiation. The main results of this paper provide novel evaluations and exact calculations of regular/Fr\'echet subgradients and their singular counterparts for general classes of marginal functions via their given data. The obtained results are applied to establishing new calculus rules for such subgradients and necessary optimality conditions in bilevel programming

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          Author and article information

          Journal
          31 May 2024
          Article
          2405.20737
          179a20ee-3bcd-4da8-8bdb-ac3d9fd5ecbc

          http://creativecommons.org/publicdomain/zero/1.0/

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          Custom metadata
          49J52, 49J53, 90C31
          math.OC

          Numerical methods
          Numerical methods

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