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

Patrick L. Combettes; Lilian E. Glaudin

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arXiv · 1704.03563

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

Patrick L. Combettes·Lilian E. Glaudin

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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.

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Patrick L. Combettes, Lilian E. Glaudin. 2017-04-11. Quasinonexpansive Iterations on the Affine Hull of Orbits: From Mann's Mean Value Algorithm to Inertial Methods. https://arxiv.org/abs/1704.03563

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