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Maximal monotonicity of the subdifferential of a convex function: a direct proof

Milen Ivanov, Nadia Zlateva

Abstract

We provide a new proof for maximal monotonicity of the subdifferential of a convex function.

Maximal monotonicity of the subdifferential of a convex function: a direct proof

Abstract

We provide a new proof for maximal monotonicity of the subdifferential of a convex function.

Paper Structure

This paper contains 2 sections, 2 theorems, 18 equations.

Table of Contents

  1. Introduction
  2. Proof of the main result

Key Result

Proposition 1

Let $X$ be a Banach space and let $f:X\to\mathbb{R}\cup\left\{ +\infty\right\}$ be a proper, convex and lower semicontinuous function. If $f:X\to\mathbb{R}\cup\left\{ +\infty\right\}$ satisfies then $0\in\partial f(0)$.

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Theorem 2
  • proof