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Proto-Differentiation of Subgradient Set-Valued Mappings

Published online by Cambridge University Press:  20 November 2018

René A. Poliquin
René A. Poliquin*
Affiliation:
University of AlbertaEdmonton, Alberta
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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.

Keywords

49A52
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 3 , 01 June 1990 , pp. 520 - 532
Copyright
Copyright © Canadian Mathematical Society 1990

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