Proto-Differentiation of Subgradient Set-Valued Mappings

Poliquin, René A.

Canadian journal of mathematics, Tome 42 (1990) no. 3, pp. 520-532

Résumé

Set-valued mappings arise quite naturally in optimization and nonsmooth analysis. In optimization, typically one has a family of optimization problems that depend on some parameter. One can then associate to this family of problems the set-valued mappings that assign to the parameter the set of optimal solutions, the set of feasible solutions or the set of multipliers. Many of these set-valued mappings encountered in optimization have been shown to be “proto-differentiable” (see Rockafellar [16]) i.e., in some sense these set-valued mappings are “differentiable”. Using estimates provided by the proto-derivatives, see Proposition 2.1, one can then obtain information on how the sets depend on the parameter. The concept of proto-differentiation is described in Section 2.

Détail

DOI : 10.4153/CJM-1990-027-2

Mots-clés : 49A52

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