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Forward-backward-forward dynamics for bilevel equilibrium problem

Kanchan Mittal, Pankaj Gautam, V. Vetrivel

Abstract

We introduce a forward-backward-forward (FBF) algorithm for solving bilevel equilibrium problem associated with bifunctions on a real Hilbert space. This modifies the forward-backward algorithm by relaxing cocoercivity with monotone and Lipschitzness. Further, we present the FBF dynamical system and investigate the generated trajectory's existence, uniqueness and weak convergence. We illustrate the proposed method for equilibrium problem under saddle point constraint.

Forward-backward-forward dynamics for bilevel equilibrium problem

Abstract

We introduce a forward-backward-forward (FBF) algorithm for solving bilevel equilibrium problem associated with bifunctions on a real Hilbert space. This modifies the forward-backward algorithm by relaxing cocoercivity with monotone and Lipschitzness. Further, we present the FBF dynamical system and investigate the generated trajectory's existence, uniqueness and weak convergence. We illustrate the proposed method for equilibrium problem under saddle point constraint.
Paper Structure (7 sections, 17 theorems, 131 equations, 1 algorithm)

This paper contains 7 sections, 17 theorems, 131 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Convergence of Forward-backward-forward method from discrete perspective
  4. Forward-backward-forward method from continuous perspective
  5. Existence and Uniqueness of trajectory
  6. Convergence of the trajectory
  7. Application to Bilinear Saddle Point Problem

Key Result

Lemma 1

Oe

Theorems & Definitions (32)

  • Definition 1
  • Definition 2
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Proposition 1
  • Proposition 2
  • proof
  • Corollary 1
  • ...and 22 more