2017/04/11 by Combettes, Patrick L., Glaudin, Lilian E. · 2 citations
#47H09 #65K05 #90C25 #FOS: Mathematics #Optimization and Control (math.OC) #Primary 65J15 #Secondary 47H05
paper · doi:10.48550/arxiv.1704.03563
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.