Quasinonexpansive Iterations on the Affine Hull of Orbits: From Mann's Mean Value Algorithm to Inertial Methods

Abstract

Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasinonexpansive operators to a point in the affine hull of the orbit generated up to the current iterate. This investigation unifies several algorithmic constructs, including Mann's mean value method, inertial methods, and multi-layer memoryless methods. It also provides a framework for the development of new algorithms, such as those we propose for solving monotone inclusion and minimization problems.

References in corpus (2)

• The rate of convergence of Nesterov's accelerated forward-backward method is actually faster than $1/k^2$
• Mean value iterations for nonlinear elliptic Cauchy problems

Cited by in corpus (4)

• Fixed Point Strategies in Data Science
• Non-ergodic Convergence Analysis of Heavy-Ball Algorithms
• Heavy-ball Algorithms Always Escape Saddle Points
• Forward-backward algorithms with different inertial terms for structured non-convex minimization problems