Decomposition by partial linearization in multiuser systems

Gesualdo Scutari, Francisco Facchinei, Daniel Pérez Song, Daniel P. Palomar, Jong-Shi Pang

Abstract: We propose a decomposition framework for the distributed optimization of general nonconvex sum-utility functions arising in the design of wireless multi-user interfering systems. Our main contributions are: the development of the first provably convergent Jacobi best-response algorithm, where all users simultaneously solve a suitably convexified version of the original sum-utility optimization problem; the derivation of a general dynamic pricing mechanism that provides a unified view of existing pricing schemes that are based, instead, on heuristics; and a framework that can be easily particularized to well-known applications, giving rise to practical algorithms that outperform all existing ad-hoc methods proposed for very specific problems. Our framework contains as special cases well-known gradient algorithms for nonconvex sum-utility problems, and many block-coordinate descents schemes for convex functions.