Title: Chapter 4 Differentiability and Subdifferentiability: Characterization of Optimal Solutions
Abstract: Publisher SummaryThis chapter introduces the concepts of differentiability in the framework of optimization theory. It presents the minimal set of a convex function as the subdifferential of its conjugate function at zero. The main justification of the concept of differentiability (in the framework of optimization theory) is the variational principle, which allows replacing a minimization problem by an equivalent problem in which the loss function is linear. In the case of convex functions, the subdifferential is a generalization of the concept of gradient. The chapter introduces the “intermediate” concept of a function differentiable from the right and discusses how it is related to the concept of subdifferentiability.
Publication Year: 1979
Publication Date: 1979-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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