F. J. Aragón Artacho, R. Campoy García, C. López Pastor
In this work, we present a methodology for devising forward-backward algorithms for minimizing the sum of a finite number of convex functions. We extend recent techniques to cover the case involving a finite number of smooth functions, which should be directly evaluated through the gradient instead of computing their proximal mapping. The algorithms are induced by three graphs that determine how the algorithm variables interact with each other and how they are combined to compute the iteration. The hypotheses on these graphs ensure that the algorithms obtained have minimal lifting and are frugal, meaning that the ambient space of the underlying fixed point operator has minimal dimension and that each proximal mapping and each gradient is evaluated only once per iteration. This framework allows to recover some known methods, as well as generating new ones.
Palabras clave: Forward-backward algorithm, Frugal splitting algorithm, Minimal lifting
Programado
Optimización Continua I
10 de junio de 2025 11:30
MR 3