The Subdifferential of a Convex Function

Adina Chirilă (), Marin Marin and Andreas Öchsner
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Adina Chirilă: Transilvania University of Braşov, Department of Mathematics and Computer Sciences
Marin Marin: Transilvania University of Braşov, Department of Mathematics and Computer Sciences
Andreas Öchsner: Esslingen University of Applied Sciences, Faculty of Mechanical Engineering

Chapter Chapter 4 in Distribution Theory Applied to Differential Equations, 2021, pp 37-55 from Springer

Abstract: Abstract In this chapter, the first section presents the definitions of Gateaux differentiable functions and of Frechet differentiable functions and the concept of subdifferentiability. Monotone and maximal monotone operators are defined. Minty’s theorem is proved. The subdifferential is shown to be a maximal monotone operator. The conjugate function is used to transform a minimization problem into a maximization problem and conversely. Finally, the additivity of the subdifferential is studied.

Date: 2021
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DOI: 10.1007/978-3-030-67159-4_4

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